Arrange a rack in the middle of the oven and heat the oven to 350ºF. Line the bottom and all 4 sides of a 9x9-inch square baking pan with 2 sheets of parchment paper, positioning them perpendicular to each and hanging over all four sides by at least 1 inch to form a sling.

Combine 1 tablespoon finely grated lemon zest and ¼ cup granulated sugar in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Use your fingers to rub the zest into the sugar until fragrant. Add 12 tablespoons room-temperature butter and ½ teaspoon kosher salt. Beat with the paddle attachment on medium speed until creamy, about 2 minutes. Scrape down the sides of the bowl with a flexible spatula.

Add 1 ¾ cups all-purpose flour. Beat on medium speed until fine crumbs of dough form, 30 seconds to 1 minute. Transfer to the baking pan and use your hands to press into an even layer.

Bake until the crust is light golden-brown around the edges, 15 to 22 minutes. Meanwhile, make the filling.

Crack 4 room-temperature large eggs into a medium bowl and whisk until beaten. Add 1 tablespoon finely grated lemon zest, ¾ cup lemon juice, 1 ½ cups granulated sugar, and ½ teaspoon kosher salt to the bowl of eggs. Whisk until smooth. Sift ⅓ cup all-purpose flour over the mixture and whisk until smooth and combined.

When the crust is ready, immediately pour in the filling while the crust is hot. Bake until the filling is just set with a slight wiggle in the center, 18 to 20 minutes. Place the pan on a wire rack and let cool for about 1 hour. Refrigerate for at least 3 hours or up to overnight.

Grasping the excess parchment, lift the slab out of the baking dish and place on a cutting board. Cut into 16 pieces, dipping the knife in hot water and wiping it dry between each cut for the cleanest-looking pieces. Right before serving, place some powdered sugar in a fine-mesh strainer and generously dust over the lemon bars in an even layer.