Preheat the oven to 350°F (175°C).
In a medium bowl, combine the flour and powdered sugar. Add the softened butter and mix until the mixture resembles coarse crumbs.
Press the mixture into the bottom of a greased 8x8-inch baking dish to form the crust.
Bake the crust in the preheated oven for 15 minutes or until lightly golden.
In a separate bowl, whisk together the eggs, granulated sugar, lemon juice, lemon zest, and baking powder until well combined.
Pour the lemon mixture over the baked crust.
Return to the oven and bake for an additional 20-25 minutes, or until the filling is set and the edges are lightly golden.
Allow the lemon bars to cool completely in the baking dish on a wire rack.
Once cooled, dust with powdered sugar if desired, cut into squares, and serve.