Preheat your oven to 350ºF. Using a sharp knife, slit the backs of your sausages and remove the casing from the meat. Put the meat in a skillet, over medium-high heat and break the sausage into crumble size. Cook until browned. Remove the sausage from the pan and reserve. Add the potatoes to the sausage grease (which you have meticulously left in the skillet and not with the reserved sausage). Let them cook until tender, stirring occasionally, about 15 minutes.
In a large bowl, beat together the eggs, sausage, potatoes, green chilies and cheese. Pour into an oven-safe glass or ceramic dish. I used a 9×9 Pyrex. Bake until the eggs are set, about 20 minutes.