Preheat the broiler.

Place a 12-inch ovenproof skillet on the stovetop, over medium-high heat, and add olive oil and butter.

When the butter is melted, add the potatoes and a sprinkle of salt and pepper.

Cook the potatoes, stirring frequently, until they begin to soften, about 5 minutes.

Add the mushrooms, green onions, garlic and thyme.

Cook until the mushrooms have released their liquid and are dry, about 4 minutes.

In the meantime, in a medium bowl, whisk together the eggs, milk, Parmesan, salt, pepper and red pepper flakes. Set aside.

Spread the mushroom mixture evenly over the bottom of the pan and sprinkle the feta over the top.

Pour the eggs evenly over the vegetables and reduce the heat to low.

Cover the pan and cook for two minutes.

Remove the lid and transfer the pan to the broiler.

Broil until the top is lightly browned and the eggs have firmed up in the center, about 4 minutes.

Remove the frittata from the oven and let it rest for 3 minutes.

Sprinkle with feta, parmesan, red pepper and thyme.

Serve hot or at room temperature.