Adjust an oven rack to middle position, then preheat oven to 375 degrees (F). Spray a 9 x 5 inch loaf pan with non-stick baking spray; set aside.: The air in the oven should feel steadily warm as it reaches 375 degrees F , and you will notice a faint mineral scent as the heating elements engage. Preheating ensures the batter hits a consistent environment, so the loaf rises evenly and forms a proper crust. If the oven is not fully preheated before the pan goes in, the cake may bake unevenly, causing a dome that cracks harshly. A good check is to let the oven reach temperature and then insert the pan; you should hear no dramatic temperature shift. Use the middle rack to allow even circulation and browning.
Melt the butter in a small saucepan over medium heat. Pour melted butter into a large bowl, then whisk in both sugars. Add in vanilla extract, lemon extract, lemon zest, and lemon juice and beat well. Add in the eggs and yolks, one at a time, beating well after each addition.: At this stage you will feel the warmth from the melted butter and smell its nutty aroma as it cools slightly. Whisking in both granulated sugar and light brown sugar dissolves the crystals and creates a glossy base, while the volatile oils from the lemon zest release a fragrant citrus perfume. Adding the eggs one at a time builds a stable emulsion, which traps air and contributes to a tender rise. If you whisk too aggressively, the mixture may look frothy, which is okay, but be careful not to overmix once flour is added. A common mistake is adding all the eggs at once, which can break the emulsion; add them slowly to maintain a cohesive batter.
In a separate medium-sized bowl combine the cake flour, salt, and baking powder. Add dry ingredients to wet ingredients and gently whisk together until just combined.: When you sift or whisk the cake flour with salt and baking powder , you are lightening the dry mix so it blends evenly. As you fold the dry into the wet, aim for a ribbon like stream that slowly disappears; the batter should be glossy and slightly thick, not overworked. The gentle motion protects the delicate crumb by minimizing gluten development, which keeps the loaf tender. If you keep stirring until every streak is gone, you risk a tougher texture. A telltale sign of overmixing is a batter that becomes elastic and pulls away in strings.
Pour batter into prepared pan and smooth the top with a rubber spatula. Bake for 20 minutes, then reduce oven temperature to 325 degrees and continue baking for about 40 minutes, or until the top is golden brown and a cake tester inserted in the center comes out clean. Cool cake in the pan for 15 minutes before transferring it to a cooling rack to cool completely (about 1 hour).: As you transfer the batter into the greased 9 x 5 inch pan, the surface should be glossy and slowly settle when smoothed. During the first 20 minutes at 375 degrees F the cake gains initial oven spring; you will hear faint crackling and see the edges pulling slightly from the pan. After lowering to 325 degrees F , the loaf continues to bake through more gently, developing an even golden brown top. The center should no longer jiggle and a cake tester should come out clean, indicating the crumb set. Allowing the cake to rest in the pan for 15 minutes helps it firm up for a clean release, while the full hour on a rack ensures it is completely cooled before frosting. A common trap is frosting a warm cake, which melts the frosting and yields a soggy finish; always wait until the loaf is room temperature.
In the bowl of a stand-mixer fitted with the paddle attachment, or in a large bowl using an electric handheld mixer, beat the cream cheese, butter, and lemon extract on medium-high speed until completely smooth; about 2 minutes. Reduce the speed to low and gradually add the sifted confectioners' sugar. Once all of the sugar has been added beat on high-speed for 1-2 minutes. If the frosting appears too thin, add a little more confectioners' sugar, 1/4 cup at a time. Once the cake has completely cooled, spread the frosting over the top of cake and decorate with lemon slices, if desired. Slice and serve! Store this cake in the fridge, covered, for up to 3 days.: When you begin, the bowl will emit a cool creamy scent from the softened cream cheese and butter , and after about two minutes the mixture should look pillowy and uniform, with no lumps. Smoothness is critical because lumps in the frosting will affect spreadability and mouthfeel. Keep beaters scraping the sides so everything becomes evenly aerated. A frequent issue is using cold cream cheese which leaves curdled lumps; ensure both ingredients are very soft but not melted.
Reduce the speed to low and gradually add the sifted confectioners' sugar. Once all of the sugar has been added beat on high-speed for 1-2 minutes: Adding the confectioners' sugar slowly prevents a flour like cloud and ensures a smooth, silky frosting. As the sugar incorporates, the mixture will thicken and become glossier, and the high speed at the end tightens the texture so it spreads cleanly. Taste and adjust sweetness carefully, since too much sugar will mask the lemon notes. If you overbeat for too long, the frosting can become overly aerated and lose structure, so stop once it reaches a silky consistency.
If the frosting appears too thin, add a little more confectioners' sugar, 1/4 cup at a time: The right frosting should cling to the spatula and slow drip rather than pour. Adding extra confectioners' sugar thickens it without making it gritty, but add sparingly to avoid a cloying finish. If your kitchen is very warm, chilling the frosting briefly can help it firm up. A mistake here is adding liquid to fix thin frosting, which only thins it further.
Once the cake has completely cooled, spread the frosting over the top of cake and decorate with lemon slices, if desired: The cool loaf should feel room temperature to the touch and the top will be slightly springy. Spreading the frosting slowly with a spatula gives a smooth finish; you may hear a soft dragging sound as the blade glides. Decorate minimally with thin lemon slices if you like a fresh look, but avoid too many wet slices which can weep onto the frosting. Placing thick slices can press into the frosting and make it uneven, so aim for thin, gently arranged slices.
Slice and serve! Store this cake in the fridge, covered, for up to 3 days: On the plate, the loaf should show a tight, uniform crumb and a silky frosting edge. Chilling helps the frosting set and improves sliceability, and the cake will hold its shape when properly cooled. Keep it covered so it does not absorb fridge odors. A common mistake is leaving the loaf uncovered, which leads to a dried crust over time.