1. Warm oil in a skillet over medium heat. Add onion; sauté until tender and golden, 6 to 8 minutes. Add garlic; sauté 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.
2. Remove skillet from heat and stir in mustard and Cheddar. Season with salt and pepper. Let cool completely.
3. 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.
4. Put racks in lowest positions in oven; preheat to 425ºF. In a bowl, whisk egg with 1 tsp. water. Brush top of pies with egg wash. Bake until puffed and golden, 15 to 20 minutes.