1. Wash and trim the tough ends of the asparagus.
Blanch for 3 minutes in boiling salted water, then plunge into cold water, drain, and set aside.
2. Beat the eggs in a bowl with the crème fraîche, then season with salt and pepper.
3. Heat the olive oil in a skillet, pour in the beaten eggs, and cook over low heat, stirring lightly.
4. Arrange the asparagus on the omelette and sprinkle with grated Parmesan.
5. Cook until reaching the desired texture, then sprinkle with thyme.
6. Serve the asparagus and Parmesan omelette.