Preheat the oven to 350° F. Line a 9×13 inch baking dish with parchment paper and set aside.: As the oven warms, you will notice a gentle hum from the heating elements and the temperature stabilizing. This step ensures the oven is evenly hot, which is crucial so the crust begins baking immediately and sets properly. The sound of the oven clicking off and the slight warmth when you open the door are small cues that it is ready. A common mistake is placing the pan in before the oven reaches the full temperature, which can yield an underbaked, soggy base. Using parchment makes it easy to lift the bars out later, and lining the pan now means you can move quickly once the dough is ready.
Add the butter to a large mixing bowl. Add in the granulated sugar and use a hand-held mixer or whisk to cream together the butter and sugar until well-combined.: At this point you will feel the slightly warm melted butter and the grainy texture of sugar as they come together into a cohesive mixture. The aroma will be rich and buttery, and the mixture should look glossy rather than oily. Properly combining these two ingredients helps the crust bind when you press it into the pan. Avoid overbeating into a foam; overworking can change the texture of the crust. If the butter cools and firms too fast, a quick gentle warm will make it workable again.
Mix in the flour and salt.: When you add the all purpose flour and the sea salt , you will notice the dry flour absorb the melted butter , forming a crumbly, slightly sticky dough. Use a spatula to fold and combine until no dry patches remain, and the mixture holds together when pressed. The flour provides structure, and the salt enhances flavor, so ensure even distribution. Be careful not to overmix to avoid developing too much gluten, which would make the crust tougher. If the dough seems too dry, a teaspoon of melted butter can bring it together.
Press the crust into the bottom of the prepared baking pan and bake for 15-20 minutes, or until just beginning to lightly brown around the edges. While the crust is baking, prepare the filling.: As you press the dough, feel for an even thickness across the pan, and listen for the slight rustle as the parchment settles. When the crust bakes, watch for the edges to gain a faint golden tone and for the surface to appear set rather than glossy. That gentle browning signals the right balance between tenderness and crispness. A common error is uneven pressing, which causes inconsistent baking. Rotate the pan halfway through if your oven has hot spots to ensure even color.
Add the eggs and sugar to a large mixing bowl. Use a hand-held mixer to mix the eggs and sugar until well-combined.: Begin this step by cracking the room temperature eggs into a bowl and adding the granulated sugar . As you mix, the texture will change from separate liquids into a pale, slightly thickened blend, and the sound will shift to a steady whisking hum. This initial emulsification helps the filling become uniform and smooth. If you under-mix, the filling may bake unevenly. Scrape the bowl sides to ensure all the sugar is incorporated into the eggs .
Add in the lemon juice and vanilla and mix until well-combined. Mix in the flour until combined.: Pouring in the fresh lemon juice releases an immediate citrus scent, and you will notice the mixture brighten in color. The clear vanilla extract adds a rounded aroma that tames the acidity slightly. Stir in the small amount of all purpose flour last to help the filling thicken and stabilize. The batter should be smooth and slightly viscous. Avoid overmixing after adding the flour, as that can create a dense result. If the mixture has lumps, a quick whisk will smooth them out.
Pour the filling mixture over the cooked crust and return to the oven to bake for 20-22 minutes, or until the filling is set.: When you pour, watch how the filling settles over the warm crust, smoothing into the corners. As it bakes, the surface will stop jigging and take on a faint sheen, and the center should be only slightly wobbly. The smell becomes sweet and tart, with buttered notes underneath. Overbaking will dry the filling and create cracks, while underbaking yields a runny center, so use the gentle wobble as your guide. If the top begins to brown too quickly, tent loosely with foil.
Remove from the oven and allow to come to room temperature before placing in the fridge to chill for 2 hours. Dust the bars with powdered sugar if desired and remove from pan before cutting into squares.: Cooling lets flavors settle and the filling firm. At room temperature you can notice the fragrant lemon aroma mellow slightly. Chilling for the full two hours ensures clean, even slices and a silky mouthfeel. Before cutting, run a knife along the parchment edges to loosen the slab, then lift it out. Dust with the optional confectioner's sugar just before serving for a delicate finish. A common slip is slicing too soon, which will produce messy pieces, so patience here pays off.