Arrange a rack in the middle of the oven and heat to 350°F. Line a 9×9-inch pan with two sheets of parchment paper positioned perpendicular to each other, hanging over all sides to form a sling.
Combine 1 tablespoon lemon zest and 1/4 cup granulated sugar. Rub the zest into the sugar with your fingers until fragrant. Add the butter and 1/2 teaspoon salt, and beat until creamy, about 2 minutes.
Add 1 3/4 cups flour and beat until fine crumbs form, 30 seconds to 1 minute. Press into an even layer in the pan.
Bake the crust until light golden-brown around the edges, 15 to 22 minutes. Meanwhile, make the filling.
Whisk the eggs until beaten. Add 1 tablespoon lemon zest, the lemon juice, 1 1/2 cups sugar, and 1/2 teaspoon salt, and whisk until smooth. Sift 1/3 cup flour over the mixture and whisk until combined.
As soon as the crust is ready, immediately pour the filling over the hot crust. Bake until just set with a slight wiggle in the center, 18 to 20 minutes.
Cool on a wire rack about 1 hour, then refrigerate at least 3 hours or overnight.
Lift out using the parchment and cut into 16 pieces, dipping the knife in hot water and wiping dry between cuts. Dust generously with powdered sugar right before serving.