Preheat oven to 375 degrees.
Slit 4 cans of green chilies lengthwise, remove seeds and drain well on paper towels. Insert cheese lengths into green chilies.
Separate refrigerator biscuits and roll each flat enough to cover each chili separately and seal well. Place wrapped chilies in casserole and bake at 375 degrees for approximately 10 minutes (until dough is halfway cooked).
Remove casserole from oven and place leftover slit chilies flat on top of each relleno. Then saute onion in 1 tablespoon olive oil and put onion on top of chilies. Add shredded Cheddar/Monterey cheese.
Beat egg whites and fold in egg yolks. Spread mixture over Monterey/Cheddar cheese and bake 15 more minutes or until egg whites are golden brown.
Let stand 10 minutes before serving with chunky salsa. Cut with sharp knife and dish out with spatula.
