Toast chilies over gas flame, turning frequently. Remove from heat. Bring water and vinegar to boil in heavy medium saucepan. Add chilies. Remove from heat. Let stand until softened, about 20 minutes. Heat oil in heavy large skillet over medium heat. Add garlic, oregano, coriander and cumin and stir until fragrant. Add tomatoes and cook until soft. Transfer to processor. Add chilies, soaking liquid and half of onion. Puree until smooth. Season to taste with salt and pepper.
Preheat oven to 350 degrees F. Pour vegetable oil into large skillet and heat over medium heat. One at a time dip tortillas into sauce and shake off excess. Transfer tortillas, one at a time, to skillet and cook 10 seconds on each side. Drain on rack.
Combine cheeses in medium bowl. Reserve 1/2 cup cheese. Divide remaining cheese into 12 portions. Spoon onto lower half of each tortilla. Sprinkle remaining onion over. Roll up each tortilla to form tube.
Arrange on baking sheet, seam side down. Bake until cheese melts, about 3 to 5 minutes. Heat remaining sauce. Spoon onto 4 plates. Top with 3 enchiladas. Sprinkle with remaining cheese and cilantro and serve.
c.1996, M.S. Milliken & S. Feniger, all rights reserved