Toast the chiles and cumin in a large skillet over medium-low heat, stirring often to prevent scorching, until they become highly fragrant, about 2 minutes.

Transfer the toasted spices to a spice grinder and let them cool for 5 minutes, then add the garlic powder and oregano and grind until a fine powder forms.

Heat the oil in the same skillet over medium-high heat until it shimmers. Stir in the ground chile mixture, flour, salt, and pepper and cook until the spices are fragrant and the color has deepened slightly, about 1 minute.

Slowly whisk in the broth and bring to a simmer. Reduce the heat to medium-low and cook, whisking often to prevent lumps, until the sauce has thickened and reduced to about 1 1/2 cups.

Whisk in the vinegar and season with additional salt and pepper to taste, then remove from the heat and cover to keep the sauce warm.

Heat the oven to 450°F and spread a small amount of the sauce over the bottom of a 13 by 9-inch baking dish. Combine the Monterey Jack and cheddar in a bowl, setting aside a half-cup of the mixture for the topping.

Brush both sides of the tortillas with oil and stack them together. Wrap the stack in a damp dish towel and microwave until the tortillas are warm and pliable, about 1 minute.

Spread a portion of the cheese mixture across the center of a warm tortilla and sprinkle with a tablespoon of onion. Roll the tortilla tightly and place it seam-side down in the baking dish, arranging them in two columns.

Pour the remaining sauce over the top to cover the tortillas completely and sprinkle with the reserved cheese. Cover the dish tightly with greased foil and bake until the sauce is bubbling and the cheese has melted.

Sprinkle the top with the remaining onion and serve immediately while the cheese is hot and pulling.