Grease a 9-by-13-inch casserole dish with butter and set aside.
Divide the olive oil between two medium skillets, and heat both over medium-high heat. Add the spicy and sweet breakfast sausages to one skillet and 8 of the hash brown patties to the other. Cook the sausage, breaking it up with a wooden spoon, until browned, 8 to 10 minutes; remove to a paper-towel-lined plate. Cook the hash brown patties until browned; remove to a paper-towel-lined plate. Arrange the hash brown patties in the bottom of the prepared casserole dish.
In a large bowl whisk together the eggs, milk, garlic powder, some salt and pepper, and the cheddar, Monterey Jack and some salt and pepper. Pour the mixture over the patties and top with the cooked sausage. Cover the casserole and refrigerate overnight.
Preheat the oven to 350 degrees F.
Crumble the 2 remaining hash brown patties over the top of the casserole and sprinkle with extra shredded cheese. Bake until the top is browned, 40 to 50 minutes.