Preheat oven to 350°F. Spray a 9x13-inch pan with cooking spray and set aside.
In a large bowl combine 2 cups all-purpose flour, 1 cup powdered sugar, and 1 cup room-temperature butter. Use a pastry cutter, two forks, or your fingertips to cut the butter into the dry ingredients until the mixture is crumbly and holds together when pressed.
Press the crumb mixture evenly into the bottom of the prepared 9x13 pan to form the crust.
Bake the crust on the middle oven rack for 15–20 minutes, or until the edges are lightly golden. Remove from oven but leave the oven on.
While the crust bakes, make the filling: in a separate medium bowl whisk together 2 cups granulated sugar and 4 large eggs until blended.
Add 1/4 cup melted butter, 1/4 cup milk, the zest of one large lemon, 1/4 cup lemon juice, 1 tablespoon flour, 1 tablespoon cornmeal, and 1/2 teaspoon salt to the sugar–egg mixture. Stir until smooth and evenly combined.
Fold 1 cup sweetened flaked coconut into the filling so it is distributed evenly.
Pour the filling over the hot baked crust and spread gently with a spatula to level.
Return the pan to the oven and bake for 25–30 minutes, or until the center is set (the surface should look mostly firm with only a slight jiggle).
Remove from oven and place the pan on a wire rack. Cool at least 30 minutes. Sprinkle with the remaining powdered sugar and cut into squares to serve.