Preheat the oven to 325 degrees F (165 degrees C).

Melt butter in an oven-safe skillet over medium heat. Stir in asparagus and olive oil; cook until tender, about 10 minutes. Stir in mushrooms; cook about 5 minutes.

Whisk eggs, water, and thyme together in a bowl; pour into the skillet. Reduce heat to low; cover and cook 5 minutes.

Transfer skillet to the preheated oven; bake until eggs are no longer runny, 10 to 15 minutes. Top frittata with mozzarella cheese and Parmesan cheese. Turn on the broiler and broil until cheeses melt and are lightly browned.