2 cups plus 3 tablespoons all-purpose flour
3/4 cup powdered sugar
1/2 teaspoon fine salt
2 sticks (8 ounces) cold unsalted butter, cut into small pieces, plus more for coating the baking dish
1 3/4 cups granulated sugar
6 large eggs
3/4 cup freshly squeezed lemon juice (from 5 medium lemons)
2 teaspoons finely grated lemon zest (from 1 medium lemon)
Heat the oven to 350°F and arrange a rack in the middle. Coat a 13-by-9-inch baking dish with butter; set aside.
Place 2 cups of the flour, the powdered sugar, and 1/4 teaspoon of the salt in the bowl of a food processor fitted with a blade attachment and pulse briefly to combine. Scatter the butter pieces over the flour mixture and pulse until the dough just begins to come together, about 20 (1-second) pulses.
Crumble the dough into the prepared baking dish and, using the base of a measuring cup or a glass dipped in flour, press evenly into the pan. Bake until the crust is fully set and just starting to brown on the edges, about 25 minutes. Remove from the oven and let cool while you make the filling, at least 5 minutes. Reduce the oven temperature to 325°F.
To make the filling, combine the remaining 3 tablespoons flour, the remaining 1/4 teaspoon salt, the granulated sugar, and the eggs in a large bowl and whisk until the sugar has dissolved and the mixture is smooth, about 2 minutes. Add the lemon juice and zest and whisk until well combined.
Pour the filling over the baked crust, return to the oven, and bake until set, about 25 to 35 minutes. Remove from the oven and let cool on a wire rack. Cut into squares and serve.