Melt butter in skillet and add leeks. Cook over medium-low heat 2 minutes. Add 1/2 cup water; cook 5 minutes more or until tender. Remove from heat and allow to cool completely; drain any excess liquid.
Sprinkle flour on a clean, dry work area and roll out puff pastry to form two 12-inch squares. Cut pastry into eight 5-inch diameter circles. Place 1 slice cheese on each pastry circle. Top each with 2 Tbsp. leeks and fold pastry in half. Seal edges. Beat egg with remaining 1 Tbsp. water. Brush egg mixture on pastry; prick top surface to allow steam to escape.
Place on cookie sheet and bake 12-15 minutes, until puffed and golden.