Place a rack in middle of oven; preheat to 325°. Line an 8x8" baking pan with parchment paper, leaving overhang on all sides. Pulse 1¼ cups (156 g) all-purpose flour, ¼ cup (28 g) powdered sugar, and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a food processor to combine. Add 7 Tbsp. chilled unsalted butter, cut into pieces, and pulse until mixture is sandy with very small butter pieces. Add 1 large egg yolk and pulse until combined; mixture will be very dry looking and powdery but should hold together when squeezed in your hand.

Transfer mixture to prepared pan and spread into an even layer to fill pan. Using a flat-bottomed measuring cup or glass, pack into a compressed layer (use your fingers to get into the corners). Bake crust until golden, 27–29 minutes. Let cool 5 minutes (don’t go longer; it needs to be warm when you add the lemon mixture).

While the crust is baking, place 1 cup (200 g) granulated sugar and 2 tsp. finely grated lemon zest in a medium bowl. Using your fingers, massage zest into sugar until fragrant and lightly tinted yellow, about 1 minute. Add 3 large eggs, remaining 1 large egg yolk, and remaining 3 Tbsp. (23 g) all-purpose flour and gently whisk just until combined. Add ⅔ cup fresh lemon juice, ¼ cup whole milk, and remaining ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt; stir to combine.

Pour filling over slightly cooled crust and gently tap pan on counter to pop any air bubbles on surface. Bake until lemon mixture is set but still jiggles slightly when gently shaken, 20–25 minutes. Let lemon bar cool, then chill until cold, at least 4 hours.

Using parchment paper overhang, lift lemon bar from pan and place on a cutting board. Cut into 16 squares.

Dust lemon bars with powdered sugar just before serving. Do Ahead: Lemon bars (without powdered sugar topping) can be baked 2 days ahead. Cover and keep chilled.