Roast chiles under the broiler or on a charcoal grill, turning often, until the skin is blackened.Place them in a paper bag and close tightly.When chiles are cool enough to handle, pull away and discard seed and inside veins.
Preheat to 425.
Brush olive oil on the bottom of 10 1/2 x 7 1/2 baking dish.Line with chiles.
Cover chiles with about 2 ounces of crumbled cotija and 4 ounces of shredded cheddar.Repeat, ending with cheese on top.
In a bowl, beat 4 eggs, salt, and pepper.Pour mixture over chiles and cheese.
Cover with foil.Bake at 425 for 40 minutes or until cheese is hot and bubbly.
Remove form oven and let rest 5 tl 10 miutes to set.
Casserole can be frozen.Cut into squares and wrap well.