Prepare Pastry for a Double-Crust Pie. Divide each ball into 8 portions. Form portions into balls. Preheat oven to 400 degrees F. Grease two large baking sheets; set aside. Remove 1/2 tsp. zest and squeeze 2 Tbsp. juice from lime.
In a large skillet melt butter over medium heat. Add apples; cook 5 minutes or until softened, stirring occasionally. Stir in brown sugar and cinnamon; cook 1 minute more. Carefully add lime juice and 3 Tbsp. tequila. Simmer, uncovered, 5 minutes or until liquid is slightly thickened and apples are tender.
On a lightly floured surface, roll or press each pastry ball into a 4-inch circle. Spoon 1 Tbsp. apple mixture onto each circle just below center. Fold bottom edge of circle over filling; seal edges with a fork. Place empanadas on prepared baking sheets; prick tops with fork. Combine egg and the water; brush over empanadas. Bake 12 to 15 minutes or until golden.
In a small bowl combine powdered sugar, 1 tsp. tequila, and cayenne pepper. Stir in enough of the milk to reach drizzling consistency. Drizzle over empanadas and sprinkle with lime zest.
Pastry for a Double-Crust Pie
In a large bowl stir together flour and salt. Using a pastry blender, cut in shortening and butter until pieces are pea size. Sprinkle 1 tablespoon of the ice water over part of the flour mixture; toss gently with a fork. Push moistened pastry to the side of the bowl. Repeat moistening flour mixture, using 1 tablespoon of the ice water at a time, until all of the flour mixture is moistened. Gather flour mixture into a ball, kneading gently until it holds together. Divide pastry in half; form halves into balls.