Preheat your oven to 375°F (190°C).
Peel the lower end of asparagus with a vegetable peeler or paring knife. Cut the asparagus on the diagonal. Keep the tips intact. Reserve a few tips for garnish.
Cut most of the fat from the prosciutto, and discard it. Chop the rest of the prosciutto into a small dice and set aside.
Grate the cheese(s) and place them in a medium bowl. Add the flour and toss to coat the cheese thoroughly.
Whisk the eggs, milk, and cream together in a medium bowl.
Add the thyme, salt, pepper, and nutmeg to the custard mixture.
Spray the interior of the tart pan with baking spray.
Place the crust into the prepared pan and trim off the excess dough.
Evenly arrange the bottom parts of the asparagus in the tart pan. Sprinkle the cheese over the top.
Sprinkle half the chives on top, then add the prosciutto evenly on top. Reserve a little prosciutto for garnish.
Pour the custard gently over the top. Lay the asparagus tips on top. Gently push them down so that they are below the custard. Sprinkle on the reserved cheese. Sprinkle with remaining chives.
Place on a baking sheet and bake for 30-40 minutes. Remove from oven. Cool for 20 minutes. Garnish.