Preheat oven to 350 degrees. Butter a 13 by 9-inch baking dish, set aside.: As the oven warms, you should smell the faint warmth of the appliance and hear the quiet click as it cycles. Preheating is essential so the crust starts baking immediately on placement, which helps it set before the fillings are added. A common mistake is placing the pan in a cool oven, which can lead to an underbaked, soggy base; always wait until the oven reaches temperature. Use a light coating of butter so the shortbread releases easily after baking, and make sure the baking dish feels evenly warmed when you slide it in.
For the shortbread layer: In a mixing bowl whisk together flour, powdered sugar and salt. Using a pastry cutter or fork, cut butter into flour mixture until it resembles coarse meal.: In a mixing bowl whisk together flour, powdered sugar and salt. Using a pastry cutter or fork, cut butter into flour mixture until it resembles coarse meal. : You will notice the dry ingredients are pale and powdery before the butter is cut in, then transform into a crumbly, sandy mixture with small pea sized bits of butter . Those butter pockets melt in the oven, creating a tender, flaky texture. If you overwork the mixture so it becomes paste like, the crust can turn dense; stop when the texture looks like coarse meal. The sound changes from dry whisking to a softer, cohesive crumble as the fat incorporates.
Pour mixture into prepared baking dish and spread and pat into an even layer. Bake in preheated oven until set, about 15 - 18 minutes. Set aside to cool slightly while preparing fillings.: Pressing the crust evenly ensures uniform baking and prevents thin spots that can burn. As it bakes you'll see the edges take on a light golden hue and the aroma of warm butter will rise. Underbaking yields a doughy center, overbaking makes it brittle, so watch for a firm top that remains slightly pale. Letting it cool a bit stabilizes the base so it supports the wet fillings without sinking.
For the lemon layer: In a mixing bowl whisk sugar and flour, then add in lemon zest, lemon juice and eggs whisk until well blended. Set aside.: In a mixing bowl whisk sugar and flour, then add in lemon zest, lemon juice and eggs whisk until well blended. Set aside. : After whisking, the mixture should be glossy and smooth, and the bright citrus scent becomes prominent. The added flour and eggs help the layer thicken in the oven, creating a custardy texture. If the mixture seems separated or curdled, whisk briskly to homogenize; avoid overwhisking which can incorporate excess air and lead to bubbles on the surface during baking. Use fresh lemon juice for the best flavor profile.
For the cheesecake layer: In a mixing bowl, using an electric hand mixer set on low speed, cream together cream cheese and granulated sugar until smooth, about 30 seconds.: In a mixing bowl, using an electric hand mixer set on low speed, cream together cream cheese and granulated sugar until smooth, about 30 seconds. : When properly creamed, the cream cheese and sugar will become soft and satiny, with a faint sheen. Low speed prevents splatter and keeps the mixture dense rather than whipped. If lumps remain, scrape the bowl and continue briefly; large pieces of cream cheese will give a grainy texture in the final bake. Avoid high speed which can introduce too much air and cause cracks.
Mix in eggs one at a time adding in vanilla with second egg. Mix in 1/4 cup sour cream. Tap bowl against countertop about 10 times to release any large air bubbles.: The batter should look cohesive and glossy after each egg, and the vanilla will add a warm aroma. Tapping releases large bubbles that expand in the oven and cause uneven texture or holes in the final layer. A common error is adding eggs too quickly, which can create a curdled appearance; add them slowly and mix until incorporated. The small amount of sour cream smooths the filling and enhances creaminess.
Pour lemon filling over crust, then evenly drizzle cheesecake filling by the spoonful over lemon layer (work to evenly distribute, layers will separate once baked). Skim off any air bubbles.: When you pour, you should see the lemon layer settle into a glossy sheet. Drizzling the cheesecake filling creates pockets that will spread slightly, forming distinct layers after baking. Use a spoon to smooth any large peaks, and pop surface bubbles with a toothpick to prevent crater like imperfections. If you pour too forcefully you could disturb the crust, so work gently and keep the layers balanced.
Gently spread cheesecake filling into an even layer. Bake in preheated oven until filling only jiggles slightly, about 29 - 33 minutes.: As it bakes the top will set while retaining a faint wobble, and the kitchen will fill with a warm, rich scent. The slight jiggle indicates the center is set but still creamy, which yields a tender texture after chilling. Overbaking will dry the filling and produce a cracked surface, while underbaking causes a runny center. Aim for a uniform, gentle wobble across the pan.
Remove from oven and allow to cool at room temperature 45 minutes then transfer to refrigerator and chill at least 2 hours.: Cooling at room temperature reduces stress from rapid temperature shifts, preventing cracks. The refrigerator firming step solidifies layers for clean slicing. A common mistake is cutting too soon; if the bars are not chilled enough they will crumble and smear. Patience here yields neat squares and better mouthfeel.
For the sour cream layer: In a small mixing bowl whisk together sour cream and powdered sugar. Spread into an even layer over chilled bars.: In a small mixing bowl whisk together sour cream and powdered sugar. Spread into an even layer over chilled bars. : The topping should be smooth and slightly glossy, and spreading it over chilled bars keeps it from melting into the filling. The powdered sugar blends seamlessly, avoiding grainy texture. If the topping is too loose, blot with a paper towel and chill briefly; too stiff a topping can tear the surface when spreading, so aim for a spreadable consistency.
Cut into squares. Store in an airtight container in refrigerator.: Use a sharp knife warmed under hot water and wiped dry for clean cuts, wiping between slices to prevent dragging crumbs. Stored chilled in an airtight container, the bars keep their texture and flavor for several days. A mistake to avoid is leaving them at room temperature too long, which can soften the layers and reduce shelf life.