1Place chicken breasts in a large skillet with halved onion, smashed garlic, and enough water to cover. Bring to a boil, then reduce heat and simmer for 20 minutes until chicken is cooked through. Remove chicken and let cool, reserving 1 cup of broth. Shred the cooled chicken with two forks.
2While chicken cooks, stem and seed the dried chiles. Toast them in a dry skillet for 1 minute per side until fragrant. Place in a bowl, cover with hot water, and let soak for 10 minutes.
3Drain the softened chiles and place in a blender with 1 cup reserved chicken broth, tomato paste, cumin, oregano, and a pinch of salt. Blend until smooth.
4Heat 2 tbsp oil in a medium saucepan over medium heat. Pour the chile sauce through a fine mesh strainer into the oil, stirring constantly for 2 minutes to remove any remaining bits. Simmer for 5 minutes. Taste and adjust seasoning with salt and pepper.
5Preheat oven to 350°F. Lightly oil a 9x13 baking dish. Mix shredded chicken with sour cream and 1 cup shredded cheese in a bowl.
6Warm the corn tortillas in a dry skillet for 20 seconds per side to make them pliable. Dip each tortilla into the warm chile sauce, lay flat on a work surface, add 3 tbsp of chicken filling down the center, roll tightly, and place seam-side down in the prepared baking dish.
7Pour any remaining chile sauce over the rolled enchiladas. Sprinkle the remaining 1 cup shredded cheese over the top.
8Bake for 25 minutes until the cheese melts and the sauce bubbles at the edges. Garnish with fresh cilantro and serve hot.