Fill a 1 1/2-quart saucepan with water, add the chiles, and bring to a boil. Cook for 10 minutes, until the chiles are tender. Remove from the heat, and remove the chile stems.
Add the cooked chiles and the clove of garlic to the container of a blender, and add 1 cup of water.
Puree the chiles well, and then strain the seeds from the puree by pouring the chile sauce through a mesh colander. Discard the seeds.
Place an oven-proof serving platter next to your cooking area. Heat the vegetable oil in a 10-inch skillet.
Place a tortilla in the heated oil, and fry briefly until it is just softened, for about 10 seconds. Turn the tortilla over in the pan, and fry for another 10 seconds. Remove the tortilla from the oil, and place on the serving platter.
Place 2-3 tablespoons of cooked chicken in the tortilla, then fold the tortilla in half. Arrange all of the filled tortillas on the platter so that they overlap.
Remove the frying skillet from the heat, and allow the vegetable oil to cool a bit.
Pour all but 2 tablespoons of the vegetable oil into a separate bowl. (When the bowl of vegetable oil is cool, discard or reserve for use in another dish.)
Return the skillet with the remaining vegetable oil to the heat, and add the chile purée.
Allow to simmer over medium heat for about 10 minutes, until it reduces slightly. Season with salt and pepper.
When ready to serve, pour the chile sauce over the folded filled tortillas on the platter.
Garnish with the cheese and onions. Serve immediately.