In a medium saute pan, heat the olive oil over medium heat. Add the sausage and cook while breaking up the meat with a spatula.
When the sausage is almost brown, add the diced red paper and continue to cook while breaking up the sausage for another 2-3 minutes or until sausage is no longer pink. Drain the oil from the pan.
Place the sausage in an ungreased 13" x 9" pan, spread evenly over the bottom.
Sprinkle with the grated cheese.
Crack 12 whole eggs into two rows on top of the sausage mixture and season with salt and pepper.