Heat the oven to 350°F. Lightly grease a 8x8 square baking dish with oil or butter.
In a large skillet cook the bacon on medium heat, stirring occasionally, until it crisp. Using a slotted spoon, transfer the bacon to a plate and reserve.
Add the onion, red pepper and mushrooms to the pan drippings in the same skillet; sauté until vegetables are fragrant and soft , about 4 minutes. Season with 1 teaspoon of salt and cook 2 more minutes. Turn off the heat and let cool slightly.
In a separate bowl, beat the eggs thoroughly and whisk in the milk. Add the remaining teaspoon of salt, and black pepper. Stir in the cheese, frozen hash brown, the bacon and vegetables mixture.
Pour the mixture into the prepared baking dish.
Bake 40 to 45 minutes or the eggs are cooked through and set.