Preheat the oven to 200°C/390°F (fan). Wash the asparagus and trim off the tough ends.
Place the puff pastry sheet on a with parchment paper lined baking tray or rectangular baking tin and press into the edges and sides. Poke holes inside the dough using a fork.
Sprinkle with half of the cheese and arrange the asparagus on it. Trim the ends if they don't fit (you can use the ends for other recipes, see notes). Mix the egg, heavy cream, and spices in a small bowl and pour over the asparagus. Sprinkle with the rest of the cheese.
Bake the tart for 20 minutes until golden brown and serve warm.
Notes
Asparagus tart is best served warm. Store leftovers in the fridge and reheat them in the oven.
If you need to trim the asparagus (not the tough ends) to fit on the puff pastry, use the leftovers to make asparagus salad or asparagus pasta.