Heat a portion of the oil in a medium saucepan over medium-high heat until it shimmers but does not smoke. Add the torn chiles and cumin seeds and cook, stirring frequently, until the chiles are fragrant and the seeds are toasted, about 3 to 5 minutes.

Stir in the garlic powder and oregano. Add the flour and cook, whisking constantly, for 1 minute to remove the raw flour taste.

Whisk in the vegetable broth, salt, and pepper. Bring the mixture to a simmer and cook until the gravy has thickened and reduced slightly, about 10 to 15 minutes. Strain the sauce through a fine-mesh strainer into a bowl, pressing firmly on the solids to extract all the flavor, then stir in the vinegar.

Brush both sides of the tortillas with the remaining oil and stack them on a microwave-safe plate. Cover with a damp paper towel and microwave until the tortillas are warm and pliable, about 1 minute.

Combine the Monterey Jack, most of the cheddar, and the onion in a bowl. Adjust an oven rack to the middle position and heat the oven to 450°F. Spread a thin layer of the sauce over the bottom of a 13x9-inch baking dish.

Working with one tortilla at a time, place the cheese mixture down the center and roll tightly. Arrange the rolls seam-side down in the baking dish to keep them from unraveling.

Pour the remaining sauce over the enchiladas and sprinkle with the reserved cheddar. Bake until the sauce is bubbling and the cheese is melted and browned in spots, 10 to 15 minutes. Serve hot.