Preheat oven to 325 degrees.Mix together eggs, milk, salt, pepper, paprika and cayenne.Cut chilies in half and add a single layer of chilies on the bottom of a 9 x 13-inch baking dish. Top chilies with half the grated cheese.Repeat with another layer of chilies and another layer of cheese.Pour egg mixture all over the top.Place into a larger baking dish or rimmed baking sheet. Pour hot water in the large pan so it comes up to the level of the eggs and bake for 35 to 40 minutes, or until no longer jiggly. Cut into squares and serve with warm corn tortillas!