Roast the chiles by using metal tongs to hold them one-by-one over the flame of your stovetop until the skin is totally charred. (If you don't have a gas stove, you can use an outdoor grill OR place them on a baking sheet directly under your oven's broiler.) When totally blackened, place the chiles in a large resealable plastic bag and seal the bag to allow them to sweat for a good 20 minutes. Then use a knife to scrape off most of the blackened skin. Stem, seed and finely mince the chiles.
Butter a large cast-iron skillet generously and set over medium heat. Put 1 tortilla in the skillet and sprinkle on a third of the Monterey Jack and pepper jack cheese, evenly spreading it all the way to the edges so that the surface will be totally covered. Sprinkle on a third of the roasted chiles. Wait for the cheese to mostly melt, then fold half of the tortilla over itself. Cook for 20 more seconds, then flip the half-moon over and cook until the tortilla is buttery and golden, for 30 more seconds. Keep warm and repeat with the remaining tortillas, cheese and chiles. Cut into 4 or 5 wedges each and serve with bowls of chili.