Preheat oven to 425 F. Line a baking pan with parchment paper. In a bowl, toss asparagus in olive oil and seasonings. Roll puff pastry into a large rectangle or square that is less than 1/8 inch in thickness. Using a pizza cutter, cut the pastry into 8 squares or rectangles.
Beat one egg and brush it on the surface of the pastries with a pastry brush. Place one slice of ham over each pastry, folding if necessary so that it fits the rectangle. Top the ham with 3-4 pieces of asparagus. Sprinkle cheese over each assembly.
Pull the edges of the puff pastry over to the center to make them overlap, the filling tucked inside. Brush the outside of each pocket with egg wash. Bake at 425 F for 12-16 minutes, or until the puff pastry is lightly golden.