Mix the chilli con carne and enchilada sauce together in a small saucepan over medium-low heat, stirring occasionally as it simmers.
Heat the vegetable oil and chilli powder together in a small frying pan over medium heat. Gently lay a tortilla in the hot oil and cook until the tortilla starts to puff. Remove with a spatula and place on a plate. Immediately sprinkle about 1/4 cup cheddar cheese and 1 tablespoon chopped onion down the centre of the tortilla; roll the tortilla tightly around the mixture and place, seam-side down, into the bottom of an oblong baking dish. Repeat this process until all the tortillas are used.
Sprinkle about 2/3 of the remaining cheddar cheese over the rolled enchiladas. Pour the warm chilli mixture evenly over the enchiladas. Scatter the remaining cheddar cheese over the layer of the chilli mixture.
Bake in the preheated oven until the top is bubbling, 20 to 25 minutes.