Preheat your oven to 350°F (175°C).
In a mixing bowl, cream together the softened butter and powdered sugar.
Add the flour and mix until crumbly.
Press the mixture into the bottom of a greased 8x8 inch baking dish.
Bake the crust for 15 minutes until lightly golden.
In another bowl, whisk together the eggs, granulated sugar, lemon juice, baking powder, and lemon zest.
Pour the lemon mixture over the baked crust.
Bake for an additional 20 minutes until the filling is set.
Allow to cool completely before cutting into squares.
Dust with powdered sugar before serving.