Preheat oven to 425 degrees with rack in center position.
Roll out puff pastry to 12-inch square. Brush Dijon mustard over entire surface and sprinkle with cheese and black pepper.
Cut dough into thirds in each direction and then cut each square in half diagonally, ending with 18 triangles. Place a piece of ham on the lower third of each triangle, add a 1/2 teaspoon jam, and roll up, making sure to place each tip-side down on a parchment-lined baking sheet.
Whisk egg and 1 teaspoon water in a small bowl until lightly beaten. Brush each puff with egg wash and bake for 16 to 18 minutes until golden brown.