Heat oil in a nonstick pan over low medium heat. Add in the potatoes and get a nice golden brown on all sides, approximately 5 - 6 minutes. Add the onion and peppers; saute for 2 - 3 minutes.
Add in the chicken sausage and brown. Make little pockets using a spoon and crack the eggs into the pockets. Season with salt and pepper.
Transfer the pan to the oven underneath the oven broiler, cook about 4 - 6 minutes until the whites of the eggs are firm and divide into portions. Garnish with cheese.