Preheat the oven to 350°F (175°C). Grease a 9x9-inch baking pan generously, ensuring all corners are covered.

In a medium bowl, mix together the flour and powdered sugar. Add the softened butter, cutting it in using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Press this mixture firmly into the prepared pan, creating a uniform base.

In another bowl, whisk together the eggs, granulated sugar, lime juice, lime zest, baking powder, and salt until fully combined. The mixture should be smooth and slightly thickened. Pour this luscious filling mixture over the crust you just prepared.

Bake for 20-25 minutes, or until the filling is set and lightly golden. Keep an eye on the edges; they should appear golden brown and may start to bubble slightly.

Once baked, remove from the oven and allow to cool completely in the pan. Dust generously with powdered sugar before slicing into squares and serving.