Remove casing from sausage and add to the hot skillet. Cook until browned, using a spatula to break up into pieces as it cooks. Remove from heat and set aside.
Sauté peppers separately; cover and set aside to keep warm.
Whisk eggs together, then add to the skillet that the pepper was cooked in; cook until no longer runny, stirring frequently to scramble.
Once everything is finished cooking, layer the eggs, peppers, and sausage into serving cups.
Top with shredded cheese and serve with orange wedges on the side.