Heat olive oil and butter in a 9-inch nonstick pan over medium heat and cook asparagus, stirring occasionally, until soft but still firm to the bite, 10 to 15 minutes.
Beat eggs in a bowl until frothy. Stir in Parmesan cheese and milk; season with salt and pepper. Pour egg mixture over asparagus and cook until eggs are set, 10 to 15 minutes.
Invert frittata onto a plate and garnish with parsley.
You can use any fresh herb you like instead of parsley and dill. Cilantro and dill work well, too.
If frittata only sets on the edges and stays liquid on top, reduce heat and cover with a lid to help the center set.
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