Preheat oven to 375°F.: When you slide a pan into a properly preheated oven you get immediate, even lift, which produces a light edge and tender center. You should smell a faint warmth and your oven should beep or indicate it has reached temperature. A common mistake is not waiting for full preheat, which can cause uneven baking and excessive spreading, so always verify the oven thermostat before baking.
In a large bowl, beat cake mix, butter, shortening and egg until well combined.: As you mix, the blend should come together into a soft, cohesive dough with a uniform pale lemon hue. You will hear a steady whir from the mixer, and the aroma will shift from powdered brightness to buttery lemon. This step matters because even distribution prevents pockets of dry mix that would yield chalky bites. Watch for overmixing, which can toughen the texture, so stop once the dough is smooth and homogenous.
Using cookie scoop, scoop onto a greased cookie sheet.: When scooping, you will feel the dough hold its shape yet yield easily to the scoop, forming round mounds that sit slightly domed on the sheet. The grease on the pan helps them release after baking and encourages a gentle bottom crust. A frequent error is placing scoops too close together, leading to merging, so space them well to preserve rounded cookies.
Bake for 9-11 minutes. Let cool completely.: While baking you will notice the edges firming and the tops becoming slightly set, with the kitchen filling with a warm lemon and butter aroma. A visual cue is faint browning at the base of the cookie, while the center remains soft. Baking too long will dry them, so aim for just set edges and slightly springy centers. Pull one out to test, it should feel springy not hard.
For frosting, mix butter, powdered sugar, milk, vanilla, almond extract and lemon juice (optional) until well combined. Add more milk or powdered sugar depending on the consistency you like.: Cooling changes the texture from fragile to stable, and you will notice the cookies lose heat and firm up, making frosting easier. The scent settles into a pleasant background note, and touching a cookie should feel just warm then room temperature. Frosting warm cookies will cause sliding or melting, so resist impatience and allow full cooling to avoid a runny glaze.
ENJOY!: As you whip the frosting, it should transform into a glossy, smooth mixture that holds soft peaks if you lift the beaters slowly. The scent should be sweet with a lifted lemon hint, and the texture should coat a spoon uniformly. This technique matters because consistency defines how the frosting sits on the cookie, and if it is too thin it will pool, while too thick will be clumpy; adjust with tiny increments of milk or powdered sugar to reach the ideal spreadable body.
Add more milk or powdered sugar depending on the consistency you like: Small additions will change texture noticeably, so add in quarter teaspoon increments, observing the gloss and viscosity after each stir. You want a frosting that spreads without running, leaving a smooth surface with gentle peaks. A common pitfall is over thinning, which leads to drippy cookies, so correct by folding in more powdered sugar to thicken back up.
ENJOY!: At the finish you should taste a balanced bite of sweet frosting and lemon cake crumb, with a pleasing interplay of soft texture and bright flavor. Notice the creaminess of the frosting against the tender cookie, and the clean citrus finish that refreshes the palate. A typical oversight is storing them in a sealed container while still warm, which traps steam and softens the frosting, so let them settle before packing for best texture.