Preheat oven to 350 degrees. Spray or grease a 9×13″ baking pan generously with cooking spray or shortening.
In a large bowl, beat the butter and 1/2 cup powdered sugar till light and fluffy, about 2-3 minutes. Add flour and salt, and beat on low speed until just incorporated, about 1 minute. Press the dough evenly into the prepared pan and bake on the middle rack of the oven 20-25 minutes, or until lightly golden. Remove from the oven and cool on a work rack.
In a medium bowl, whisk the eggs and 2 cups of sugar. Add the flour and whisk until combined. Whisk in the lime juice and zest. Pour over the cooled crust, and bake 25 minutes longer, or until the filling has set. Cool completely on a wire rack. Dust with sifted powdered sugar once cooled. Cut into squares and Enjoy!