In a medium-sized bowl, whisk the eggs, and stir in two tablespoons olive oil. Set aside.
Over medium heat in an oven-safe 10” skillet, sauté onions in one tablespoon olive oil until softened and slightly browned. Add the asparagus, mushrooms, tomatoes, basil, onion powder, salt, and pepper. Sauté another 3 minutes.
Pour in the egg mixture and mix together. Place the pan in the oven for about 15 minutes; then sprinkle parmesan cheese over the top. Bake until the egg is set in the middle and cheese is melted, about 5-10 more minutes.
Remove (using an oven mitt!) from the oven. Cool for five minutes; then, using a spatula, release the frittata around the edges and under the bottom. Slice and serve.