Preheat the oven to 350 F. Line an 8x8" pan with tin foil and a light drizzle of oil.
Cut the peppers in halves, vertically, and remove the stems/seeds. Set aside.
In a large frying pan over medium heat, cook the breakfast sausage while breaking it apart with a spatula. Once browned, add the onion and cook again until the onions are softened, another 4-6 minutes. Remove from heat, add salt and pepper as needed.
Arrange the pepper halves in the prepared pan so they're level. Spoon ¼ cup of the sausage and onion mixture into each pepper, then crack one egg into each pepper. Top with cheese, and cover the entire pan with tin foil.
Bake for 25-30 minutes before removing and garnishing with green onions.
Notes
If you want a softer pepper, pre-bake the pepper halves {before adding the meat and eggs} for 10 minutes. Bake time with the eggs will depend on how done you want the egg. For a runny yolk, start with 20 minutes. For a hard-boiled egg, you may need more than 30 minutes.
Recipe by The Kitchen Paper at http://c02.ddd.mwp.accessdomain.com/sausage-egg-stuffed-peppers/