Melt the butter in a pan over medium heat. Place 1 slice of bread in the pan, cover it with the cheddar cheese slices and shredded mozzarella cheese, and place the other slice of bread on top. Fry the sandwich on both sides until golden brown.
Remove the grilled cheese sandwich from the pan and wipe the pan clean. Sprinkle the parmesan cheese into the pan in the shape of a cross, making sure that the center is about as wide as the sandwich. Place the grilled cheese sandwich in the center of the parmesan cross.
Add the red onion, bacon, bell pepper, and tomato to the pan in the spaces between the parmesan cross.
Once the parmesan cheese has melted, carefully remove the grilled cheese sandwich and parmesan cross from the pan. Place the sandwich on an upside-down glass so that the parmesan cheese hangs down and wait about 3 minutes for the cheese to harden.
Stir the sautéed vegetables and bacon together in the pan. Crack the eggs on top, add the parsley, season with salt and pepper, and scramble the mixture. Carefully lift the grilled cheese sandwich from the glass, turn it over so that the parmesan cheese crown is pointing up, and spoon the scrambled eggs over the grilled cheese sandwich in the middle.