For the crust: Preheat the oven to 350 degrees F. In a medium saucepan, melt the butter. Mix the flour and confectioners' sugar in a bowl and add the melted butter, mixing until a dough forms. Press the mixture firmly into a 9- by 13- by 2-inch pan. Bake the crust for 25 minutes.
For the filling: While the crust is baking, with an electric mixer, combine the eggs, lemon juice and zest until smooth. Add the granulated sugar, flour, baking powder and salt, and beat until smooth. Pour the mixture over the baked crust. Bake for 20 minutes more.
Remove the pan from the oven and let it cool completely. Sprinkle the top with confectioners' sugar. Cut into squares and serve.