Preheat the oven to 350°F (175°C).
Prepare a 9x9-inch baking dish by greasing it or lining it with parchment paper.
In a medium bowl, combine flour, sugar, baking powder, and salt.
Mix in the melted butter until crumbly.
Press the mixture into the bottom of the prepared baking dish to form the crust.
Bake the crust for 15 minutes until lightly golden.
While the crust is baking, whisk together eggs, lemon juice, lemon zest, and sugar in a separate bowl.
Pour the lemon filling over the baked crust, spreading it evenly.
Bake for an additional 20-25 minutes until the filling is set and slightly golden on top.
Remove from the oven and let cool completely in the pan before cutting.
Dust with powdered sugar before serving, if desired.