Preheat oven to 350 degrees.
In a medium bowl, whisk together the eggs and milk. Season with salt and pepper and set aside.
In a large 10 inch skillet heat the butter over medium high heat. Saute mushrooms, garlic and green onions for about 5 minutes until they are slightly soft. Season with salt and pepper. Add the beaten egg mixture over the vegetables ensuring that they cover the majority of the veggies. Turn the burner to medium and let the egg set for about 4-5 minutes.
Sprinkle the top with Goat cheese. Once the bottom and sides of the frittata are stable, transfer the entire skillet into a oven and bake for about 6-8 minutes. Remove from the oven once the egg is fully cooked and serve immediately.