1. Preheat oven to 400 degrees. In a 9-inch deep-dish pie plate, toss mushrooms, potatoes and oil; season with salt and pepper. Roast for 20 minutes, tossing once.
2. Meanwhile in a medium bowl, whisk together eggs, milk, mustard, hot-pepper sauce, 1/2 tsp. salt and 1/8 tsp. pepper. Stir in Cheddar and broccoli.
3. Pour egg mixture over mushrooms and potatoes and stir to distribute them. Bake until frittata is puffed and set in the middle and a paring knife inserted in center comes out clean, about 45-50 minutes.
