Chop the green and red bell peppers. Mix together the eggs, milk, and water, then gradually add in the flour. Once everything is combined, stir in the mayonnaise, chopped bell peppers, salt, pepper, and chopped parsley. Let the mixture sit for 15 minutes.
Preheat the oven to 425°F. Make a slice about 2 inches long down the center of each bratwurst sausage. Slice the cheese into strips of the same length, then stuff them inside the slit in each sausage.
Wrap each cheese-stuffed bratwurst in 2 slices of bacon, then fry them in a baking pan on all sides until the bacon is crispy.
Pour the egg mixture over the stuffed bratwurst, transfer the baking pan to the oven, and bake the breakfast casserole at 425°F for 25 minutes. While the casserole is baking, heat a pot filled with cooking oil on the stove. Peel the large yellow onion and slice it into half rings. Stir together the paprika and flour, dip the slices of onion in the mixture, then fry them in hot cooking oil until golden brown.
After 25 minutes, remove the casserole from the oven and top it off with shredded mozzarella and fried onions. Transfer the baking pan back to the oven and bake the casserole for another 10 minutes.