Preheat oven to 350 degrees F (175 degrees C).

Heat olive oil and butter in a wide non-stick frying pan over medium heat.

Add chopped onion and cook, stirring often, until onion begins to soften (about 3 minutes).

Stir in minced garlic, parsley, chopped broccoli, and dry basil.

Continue cooking, stirring often, until broccoli is bright green (about 3 minutes).

Remove from heat and stir in salt, pepper, and 2 tablespoons of the grated Parmesan cheese.

In a large bowl, beat eggs and egg whites until well blended.

Stir in broccoli mixture.

Spray a shallow 2 quart baking dish with cooking spray.

Pour the broccoli mixture into the dish.

Sprinkle evenly with the remaining Parmesan cheese.

Bake, uncovered, in a 350 degree oven until frittata is firm in the center when touched (25 to 30 minutes).

Let cool slightly before serving.