Preheat a 9-inch nonstick skillet over medium heat and add olive oil and butter. Once the butter is melted, add the asparagus and cook until they are tender but still crisp, about 10 to 15 minutes.
In a mixing bowl, whisk the eggs until frothy. Blend in the grated Parmesan cheese and milk, then season the mixture with salt and pepper.
Pour the egg mixture over the cooked asparagus in the skillet. Allow it to cook without stirring until the eggs are just set (about 10 to 15 minutes).
Carefully invert the frittata onto a serving plate and garnish with fresh parsley. DEVOUR!