Bring water to a boil over high heat in a large nonstick oven safe skillet. Add in the potatoes and onions and bring to a second boil. Reduce heat, cover, and simmer until potatoes are tender crisp, about 6 minutes.
Add in remaining ingredients, except cheese. Reduce heat to medium - low and cook until eggs are almost set, about 20 minutes. Do not stir.
While egg mixture is cooking, preheat broiler.
Move pan from stove to broiler, about 4 to 5 inches from heat, and broil for 2 minutes.
Handling carefully to avoid burns, pull out pan and top with cheese. Broil until cheese is melted, about 1 to 2 minutes. Watch carefully so it doesn’t burn.