Preheat the oven to 375°F (190°C).

Whisk together eggs, milk, garlic powder, thyme, salt, and pepper in a bowl.

Heat olive oil in an oven-safe skillet over medium heat. Add mushrooms and sauté until golden.

Stir in shredded chicken and cook for 2 minutes.

Pour the egg mixture into the skillet, spreading evenly. Sprinkle cheese on top if desired.

Cook on the stovetop until edges set, about 5 minutes.

Transfer skillet to the oven and bake for 10-12 minutes until the center is firm.

Cool slightly, slice, and serve.