Place the eggs, egg whites, milk, salt and pepper into a bowl and whisk to combine.
Heat about a tablespoon of olive oil in medium cast iron skillet over medium heat. Add the diced potatoes and chorizo. Cook, stirring occasionally until the chorizo has released some of it's gorgeous orange oil and the potatoes are just tender and golden. Sprinkle the cheese and the parsley over the top.
Pour the egg mixture the filling ingredients in the frying pan. Let cook until the bottom and sides are set (about 10 minutes depending on how hot your pan is). Place pan in the oven on the middle shelf and broil until the top is puffy and golden, about 5 minutes.
Remove from oven and let sit for about 5 minutes to rest.