Heat a large skillet over medium-high heat. Add bacon and cook for 5-7 minutes, or until almost done, stirring frequently. Add mushroom and onion and cook for an additional 5-7 minutes, or until vegetables are tender and bacon is fully cooked. Drain.
Arrange the English muffins in a single layer in a small baking dish (an 8-inch square dish or similar size works well). Top with the bacon and vegetable mixture, and then sprinkle with cheese.
In a large bowl, whisk together eggs, half-and-half, milk, and a pinch of salt and pepper. Slowly pour the egg mixture into the baking dish. Cover and refrigerate for about 8 hours.
Prior to baking, remove casserole from refrigerator and allow to sit on the counter at room temperature for about 30 minutes.
Bake casserole, uncovered, at 350 degrees F for about 35 minutes or until eggs are completely set. After about 20-25 minutes of baking time, check the casserole -- if the top is getting too brown, cover with aluminum foil for remainder of baking.