Preheat the oven to 350F.

Heat a cast iron pan over medium high heat and add the butter and oil. Once hot, add the smashed garlic clover, thyme, and mushrooms. Season with salt and pepper. Cook the mushrooms for 3 minutes until the mushrooms are soft.

Meanwhile, whisk together the milk and eggs. Set aside.

Remove the garlic and thyme from the pan. Add 1/4 tsp of salt and a few turns of pepper to the whisked eggs and mix to combine.

Turn the heat to medium and add the eggs. Slowly push the edges in towards the center. The bottom should just be set and the top should still be runny. Top with the optional cheese and chopped parsley.

Place it in the oven and bake until the cheese and melted and the eggs are cooked. Serve hot.