2 cups all-purpose flour
1/4 cup yellow cornmeal
1 teaspoon baking soda
1/2 teaspoon cream of tartar
1/2 teaspoon salt
6 tablespoons butter, softened (no substitutes)
6 tablespoons vegetable shortening
1-1/2 cups sugar, divided
2 tablespoons light-colored corn syrup
1 large egg
1 teaspoon vanilla extract
3 tablespoons plus 1/2 teaspoon grated lime peel, divided (about 4 limes)