Place oven rack in top third of oven; preheat to 350 °F. Lightly oil a 9-by-13-inch baking dish or coat with cooking spray.
Cook sausage in a large nonstick skillet over medium heat until no longer pink, breaking it up with a wooden spoon; transfer to a paper towel to drain, blotting the top with a second paper towel.
Wipe the pan clean and add oil; heat over medium-high heat. Add potatoes and saute until tender and browned, 10 to 12 minutes. (Reduce heat if necessary to prevent scorching.). Let cool slightly.
Whisk together whole eggs and egg whites in a large bowl. Add cottage, Cheddar and Parmesan cheeses, chiles, flour, baking powder, salt and pepper and whisk to mix thoroughly. Add the cooked sausage, crumbling up any large pieces, and the potatoes; mix well. Pour into the prepared dish. Bake until golden on top and set in the center, 30 to 35 minutes.