Heat oil in a nonstick pan on medium heat. Add in the onion and peppers, saute for 4 minutes. Add in the chicken sausage, saute for 2 minutes more.
Pour the eggs into the pan. Cook, without stirring, until egg mixture begins to set, approximately 1 minute. Using a heat-resistant spatula, gently lift a corner of the egg; tilt pan to allow uncooked egg to flow underneath the omelet, continue that process until there is no longer any runny egg. Fold the omelet in half and portion onto the bread and top with cheese.
Place the sandwich on a baking sheet and put it in the oven. Cook until all the cheese has melted, approximately 3 - 5 minutes.