Preheat oven to 400 degrees F. In a 9-inch pie plate, toss mushrooms, potatoes and oil. Season with salt and pepper and roast for 20 minutes, tossing once.
Meanwhile, in a medium bowl, whisk together eggs, milk, mustard, hot sauce, salt and pepper. Stir in cheese and broccoli.
When vegetables are done roasting, pour egg mixture over mushrooms and potatoes and stir to combine.
Bake until puffed and set in the middle, about 45 to 50 minutes. Cut into slices and enjoy!