Heat oven to 350F.
Beat the eggs with parsley, salt and pepper; set aside.
Heat a medium, ovenproof, nonstick skillet over mediumhigh heat. Add one tablespoon olive oil and onions, and cook until lightly browned. Remove onions from the skillet and set aside.
Wipe the skillet clean and return to heat. Add remaining olive oil to the skillet. Add eggs and cook over mediumhigh heat for 3 to 4 minutes, or until the eggs begin to set. Sprinkle onions, asparagus, potatoes, mushrooms, and tomato over the top. Sprinkle with Parmesan cheese.
Bake for 5 to 10 minutes, or until the egg is set in the center. Slide the frittata onto a serving dish and cut into quarters.
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