Sauté the vegetables. In a cast iron skillet, heat vegetable oil over high heat. Add potatoes and cook, stirring occasionally, until brown and tender. Add onions and red pepper. Continue to cook until onions are translucent. Add shredded chicken and season with salt, pepper and cinnamon.
Add the eggs. Make 4 wells in the hash. Crack an egg into each well. Top the hash with cheese.
Finish. Heat oven to 320° F. Put the hash in the oven and cook for 3-5 minutes or until eggs are cooked to your liking and cheese is melted.