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.
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.