20 dried new mexico chiles
3 tbsp. canola oil, plus more for frying
10 cloves garlic
1⁄4 cup fresh lime juice
1 tbsp. ground cumin
2 tsp. sugar
Kosher salt, to taste
12 corn tortillas
2 cups grated mozzarella
2 cups grated sharp cheddar
3⁄4 cup finely chopped red onion
1⁄4 cup finely crumbled cotija cheese
3 tbsp. crema or sour cream
Soften chiles ,Transfer chiles and 2 cups soaking water to a food processor; let cool.
Heat oven to 450˚. Heat oil in a 12″ skillet over medium heat. Add garlic; cook until golden brown, about 2 minutes. Using a slotted spoon, transfer garlic to the food processor with the reserved chiles, reserving oil in skillet. Purée chile–garlic mixture; add lime, cumin, sugar, and salt and pulse to combine. Strain through a sieve; discard solids. Transfer chile sauce to reserved skillet; heat sauce over medium heat.
Pour oil into a 10″ skillet over medium-high heat to a depth of 1⁄2″. Using tongs and working with one tortilla at a time, dip tortilla in oil; cook until slightly crisp, about 15 seconds. Drain tortilla. Dip in chile sauce to coat, and transfer to a plate. Sprinkle some of the mozzarella, cheddar, and onions along center of tortilla. Roll up enchilada. Arrange rolled enchiladas on a baking sheet; bake until cheese is melted, about 5 minutes. Divide enchiladas between 4 plates; sprinkle with cotija cheese and drizzle with crema.