Add onion; saut until tender and golden, 6 to 8 minutes.
Add garlic; saut 1 minute longer.
Add beef and cook, stirring and breaking up large pieces with the back of a wooden spoon, until no longer pink, about 5 minutes. Stir in cabbage; cook until wilted and soft, about 10 minutes.
Remove skillet from heat and stir in mustard and Cheddar. Season with salt and pepper.
Let cool completely.
Line 2 baking sheets with parchment.
Remove puff pastry from refrigerator 1 sheet at a time. Unroll pastry on a floured work surface and cut into 4 5-by-5-inch squares.
Place 1/4 cup of meat mixture in center of each square, leaving a 1-inch border. Fold into triangles; seal edges with a fork.
Place at least 2 inches apart on baking sheets; refrigerate. Repeat with remaining pastry and filling. Refrigerate pies for 30 minutes.
Put racks in lowest positions in oven; preheat to 425F. In a bowl, whisk egg with 1 tsp. water.