Peel the asparagus, cut off the woody end. Wash the asparagus, cut the stalks in half and cook in boiling salted water for about 20 minutes. In the meantime, remove the scampi (except for the tail end) from their skin.
Make a small longitudinal incision in the back and remove the intestine. Wash the scampi and pat them dry. Sprinkle with salt and pepper. Peel the garlic and press it through the garlic press. Heat the oil in a pan.
Steam garlic in it until golden brown. Add the scampi. Cook over medium heat while turning for about 5 minutes. Deglaze with white wine. Bring to the boil briefly. Toast the slices of bread until golden brown. Halve diagonally.
Drizzle with white wine stock. Put asparagus and scampi on top. Grate cheese and sprinkle over it. Slide under the preheated grill until the cheese has melted. Serve garnished with dill and lemon wedges.