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 1/2 teaspoon of the salt in the bowl of a food processor fitted with a blade attachment and pulse briefly to combine. Scatter butter pieces over flour mixture and pulse until dough just begins to come together, about 20 (1-second) pulses.
Crumble 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 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 remaining 3 tablespoons flour, remaining 1/2 teaspoon salt, granulated sugar, and eggs in a large bowl and whisk until sugar is dissolved and mixture is smooth, about 2 minutes. Add lemon juice and zest and whisk until well combined.
Pour filling over 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.