Preheat broiler. In a medium bowl combine eggs, milk, thyme, and pepper. Beat with a whisk until well mixed and evenly colored; set aside.
In a large broilerproof skillet heat oil over medium heat. Add asparagus; cook and stir about 4 minutes or until asparagus is crisp-tender. Stir in prosciutto.
Pour egg mixture over asparagus mixture in skillet. Cook over medium heat. As egg mixture sets, run a spatula around edges of skillet, lifting egg mixture so the uncooked portion flows underneath. Continue cooking and lifting edges until egg mixture is almost set (surface will be moist).
Place skillet under the broiler, 4 to 5 inches from the heat. Broil for 1 to 2 minutes or just until top is set. Sprinkle with cheese.