In a bowl, with an electric mixer at medium speed, beat butter and 1/2 cup powdered sugar until smooth. Beat in 2 cups flour until dough is no longer crumbly. Pat into a ball.
Press dough evenly into a buttered and floured 9- by 13-inch baking pan. Bake in a 350° oven until golden, about 20 minutes.
Meanwhile, in a food processor, or in a bowl with an electric mixer on medium speed, whirl or beat granulated sugar, remaining 1/3 cup flour, baking powder, grated lemon peel, lemon juice, and eggs to blend. Pour onto hot crust.
Bake until lemon mixture is no longer runny in the center (cut to test), 35 to 40 minutes. Remove from the oven and dust with remaining 2 tablespoons powdered sugar.
Let cool completely in pan, then cut into 24 bars.
Note: Nutritional analysis is per bar. The lemon squares can be chilled airtight for up to 2 days.