Preheat oven to 375 °F.
Combine dijon mustard, mayonnaise, garlic, thyme, and salt and pepper in a small bowl and mix together.
Rinse asparagus and cut about 2-3 inches off of the bottom of the asparagus.
Cut one sheet of puff pastry into 9 squares. Brush each square with dijon mustard sauce. Then fold a slice of prosciutto in half and place on the puff pastry square. Sprinkle with about 1 tbsp of cheddar cheese and place 3-4 asparagus stalks on top.
Fold one side of the puff pastry on top of the other to form a wrap (as pictured above). Brush with a beaten egg and sprinkle everything but the bagel seasoning or sesame seeds on top. Place on a parchment lined baking sheet.
Bake in the oven for 20-25 minutes, until puff pastry is golden brown and cheese is melted.