Preheat oven to 350°.
Place first 5 ingredients in a medium bowl; beat with a mixer at medium speed until creamy (about 2 minutes). Lightly spoon 1 cup flour into a dry measuring cup; level with a knife. Gradually add 1 cup flour to butter mixture, beating at low speed until mixture resembles coarse meal. Gently press two-thirds of mixture (about 1 1/3 cups) into bottom of an 8-inch square baking pan coated with cooking spray; set remaining 2/3 cup flour mixture aside. Bake at 350° for 12 minutes or until just beginning to brown.
3. Combine 2/3 cup sugar, 3 tablespoons flour, baking powder, and 1/8 teaspoon salt in a medium bowl, stirring with a whisk. Add lime juice and eggs, stirring with a whisk until smooth. Pour mixture over crust. Bake at 350° for 12 minutes. Remove pan from oven (do not turn oven off); sprinkle remaining 2/3 cup flour mixture evenly over egg mixture. Bake an additional 8 to 10 minutes or until set. Remove from oven; cool in pan on a wire rack. Sprinkle evenly with powdered sugar.