Heat the vegetable oil in a 10-inch skillet. Fry the tortilla quarters until golden brown, for about 1-2 minutes.
Remove from the vegetable oil, and drain on paper towels until all of the tortillas have been fried. Set aside in a warming drawer, or in a warm oven until the sauce is prepared.
Remove the 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.)
Combine tomatillos, garlic, and salt in a blender, and puree well.
Return the skillet with the remaining vegetable oil to the heat. Pour in the sauce, add the whole chiles and allow to simmer for 3-5 minutes until slightly reduced.
Heat your oven to 350°. In an oven-proof dish, arrange tortilla quarters.
Pour the sauce over, then sour cream, then cheese and onions. Bake in oven until bubbling, about 10 minutes. Serve hot.