Preheat oven to 350 degrees F.
In the bowl of a stand mixer, combine 2 cups of flour, 1/2 cup of confectioners' sugar, and butter until the mixture becomes dough-like. Press the dough into a 9 x 13 pan, extending it slightly up the sides (the edges should be slightly higher than the middle to prevent the filling from seeping under the crust). Bake for 20 minutes, or until the edges are golden brown. (While the crust is baking, prepare the filling since you will be immediately pouring it onto the hot crust.)
2-1/4 cups all-purpose flour, 1/2 cup (more for dusting) confectioners' sugar, 1 cup butter, room temperature
For the filling (to be made while the crust is baking), whisk together the eggs, granulated sugar, lime zest, lime juice, and salt. Fold in the remaining 1/4 cup of flour and baking powder until combined. Pour the mixture over the hot, baked crust as soon as it comes out of the oven. Immediately place it back in the oven for 25 minutes, or until set.
4 large eggs, room temperature, 2 cups granulated sugar, zest of two limes, 6 tbsps. fresh lime juice, 1/8 tsp. table salt, 1 tsp. baking powder
Remove from the oven and immediately sprinkle confectioners' sugar over the baked lime squares while they are still hot.
When completely cooled, cut into squares. (I like to refrigerate mine overnight before cutting to get perfect edges, but it is not necessary.)