Preheat your oven to 375°F. Grease or line a sheet pan with parchment paper.
Heat the olive oil in a small saucepan and sauté the mushrooms and red bell pepper for about 5 minutes, until they release their moisture. Set aside to cool slightly.
In a bowl, whisk the eggs and milk, and season with a pinch of salt and pepper. Pour the egg mixture onto the prepared sheet pan, tilting slightly to spread evenly.
Evenly distribute the the sautéed mushrooms, red bell pepper, and shredded cheese over the eggs.
Bake for about 15 minutes, until set. Remove from the oven and sprinkle with fresh parsley.
Let cool slightly, then slice into portions and serve.