Heat the olive oil in a heavy skillet and lightly saute the vegetables until hot through but not yet beginning to brown. Cool and put into a bowl with the chicken, cilantro, salt and pepper.
In a clean heavy skillet, heat about 1/4 inch of oil. One at a time, dip the tortillas in the oil and leave just long enough to soften. Drain quickly and put on a flat plate. Place about 2 to 3 tablespoons of the chicken mixture along one edge of the tortilla. Roll up and place seam side down in a shallow baking dish. Continue until all the tortillas are filled. Mix the salsa verde and chicken stock together and pour over the enchiladas. Bake in the oven at 350°for about 30 minutes, or until the sauce has reduced and is thick and the enchiladas are just beginning to brown here and there.
For chicken:Place 3 quarts water in a pot.Add 1 tsp salt, 1/2 tsp black pepper and 1 each onion and carrot roughly chopped.Bring to a boil and add chicken breats.Turn heat down to a simmer and cook until chicken is very tender and shreds easily. Strain broth and discard vegetables. Save this broth to use in this recipe.
Roasted Garlic: Place the garlic cloves in a oven proof dish and drizzle with olive oil.Roast at 350F until cloves are soft and brown, about 45 minutes.
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