Preheat the oven to 350°. Heat 1/4 cup of the oil in a large skillet until shimmering. Using tongs, dip both sides of a tortilla into the hot oil and cook just until softened, about 10 seconds; let any excess oil drip back into the pan. Drain on paper towels and set the tortilla on a work surface. Repeat with the remaining tortillas. Spoon 1 1/2 tablespoons of the cheese onto each tortilla, then loosely roll them up and arrange side by side in a 9-by-13-inch baking dish. Sprinkle with the remaining 3/4 cup of cheese and bake for about 10 minutes, or until the enchiladas are warmed through and the cheese is melted.