Double Crunch Chile Relleno Monte Cristo Sandwiches

slices 1/2-inch thick bread (I used a round of Italian)

butter

slices cheddar cheese (thin)

slices pepper jack cheese (thin)

green chiles (such as Hatch green chile, poblano or Anaheim, seeded and chopped, roasted and skinned*)

flour

eggs (lightly beaten)

salt

Vegetable oil (enough to coat the bottom of a large skillet or frying pan)