Cut off the woody ends of the asparagus, possibly peel a little in the lower third and cook in salted water with a little sugar for 3-4 minutes (depending on thickness). Drain and then cut into pieces approx. 4 cm long.
Layer the potato slices and asparagus pieces in a baking dish.
Mix the whipped cream with the parsley, garlic and half of the parmesan and season with a little salt and pepper. Pour over the gratin, sprinkle with the rest of the Parmesan and bake in the oven at 200 degrees for about 20-25 minutes.