Transfer chile ancho to a saucepan. Cover with 4 cups of water and heat to medium. Bring to a boil, reduce heat, and cook for 6 minutes, stirring halfway through cooking time. Remove from heat and let them sit for 10 minutes.
Drain the chile anchos and transfer to the blender. Add the 2 cups of chicken broth, garlic, cumin, oregano, pepper, and salt to taste. Blend on high until smooth and strain through a wire mesh strainer into a bowl.
Heat 3 tablespoons of oil to medium heat in a pan. Add the chile ancho sauce and continue cooking for 15 minutes or until the sauce reduces and thickens. If it's too thick, add a little more reserved broth. Taste for salt.
Transfer potatoes and carrots to 2 cups of lightly salted water. Cook for 10 minutes or until fork tender. Reserve. To the chicken, mix in 3 tbsps. of chile ancho sauce. Reserve.
This is a traditional way to prepare the enchiladas. Preheat 1/3 cup of oil in a large skillet to medium heat for 5 minutes. When ready, dip one corn tortilla into the chile ancho sauce and turn to coat evenly. Using the tongs, dip the tortilla in the hot oil and cook for just a few seconds on each side. Add more oil, as needed. Transfer to the serving dish and fill with shredded chicken. Roll as tight as you can. My honest opinion is that it’s more time consuming and harder to handle the tortillas when filling and rolling. See recipe notes for my easier version.
Transfer filled enchiladas to a baking dish covered with foil paper as you roll them to keep them warm. Garnish as you like with toppings listed.
Drain potatoes and carrots. Mix in a little of the chile ancho sauce. After you are done frying the tortillas, in that same pan, sauté the seasoned carrots and potatoes before serving with enchiladas.