Pour the oil into a large pot, to a depth of 2 to 3 inches, and heat to 375 degrees F. Drop in 1 tortilla at a time and fry until crisp, about 1 to 2 minutes, turning once. Remove with tongs, shake off excess oil and transfer to paper towels to drain. Repeat for all tortillas.

Heat 1 tablespoon of vegetable oil in a large skillet over moderate heat. Add the chorizo and saute for 3 minutes, or until browned. Spoon out excess fat. Add the onions and cook, stirring occasionally, until golden. Stir in the garlic and cook for 1 more minute to release its aroma. Add the tomatoes saute an additional minute. Remove from the heat and stir in the anejo cheese.

To serve, spoon warm chorizo mixture onto crisp tortillas and top with shredded lettuce.