In a large bowl, combine 2 cups flour and confectioners’ sugar; cut in butter until mixture resembles coarse crumbs. Pat into a greased 13-by-9-by-2-inch baking pan. Bake at 350 degrees for 20 minutes or until lightly browned.
In a large bowl, whisk the eggs, sugar, lime juice and peel until frothy. Combine the baking powder with remaining flour; whisk in egg mixture. Pour over crust.
Bake for 20–25 minutes or until light golden brown. Cool on wire rack. Dust with confectioners’ sugar. Cut into squares.