Preheat the oven to 425 degrees. Line a large-rimmed baking sheet with parchment paper.
Combine the cottage cheese, tarragon, and garlic in a small bowl.
On a lightly floured surface, roll the puff pastry to a 12-inch square. Cut into 9 (4-inch) squares; lightly brush with the egg.
Spoon a generous 1 tablespoon cottage cheese mixture in the center of each pastry square and top with the prosciutto.
Arrange the asparagus diagonally on top of the prosciutto. Fold the opposite corners over the asparagus and press to seal. Place on the baking sheet and lightly brush with the egg.
Bake 15 minutes or until golden brown. Serve immediately.