On a baking sheet with silicone liner or parchment paper, roll crescent dough out flat; seal perforated lines with fingers. Layer fillings down the middle third of the dough lengthwise in order: turkey, ham, cheese, garlic powder, and black pepper. Cut 1-inch slits 1 inch apart on either side of the meat and cheese, then cross strips over filling, gently pressing edges together to seal.
Preheat oven to 375 F. In a small bowl, beat egg with a splash of water and brush mixture on top of dough. Place on middle rack in oven. Bake 20 minutes, until dough is golden brown. Meanwhile, mix together mayonnaise and Dijon to make a dipping sauce. Let the rolls cool a minute or two before slicing and serving.
Per serving: 307 calories, 19 grams fat (6 grams saturated fat), 19 grams total carbohydrates, 543 milligrams sodium, 55 milligrams cholesterol, 0 grams fiber, 14 grams protein.
