Toast the dried chiles in a dry skillet over medium heat for 10-15 seconds per side until fragrant. Soak in boiling water for 20-30 minutes until soft, reserving 1/2 cup of the soaking liquid.
Char tomatoes, half the onion, and garlic in the Dutch oven with oil over medium-high heat for 3-4 minutes per side until caramelized. Remove and set aside.
Blend soaked chiles, charred vegetables, chicken broth, reserved soaking liquid, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and pepper until smooth. Strain through a fine mesh strainer.
Pat chicken dry and season with salt and pepper. Sear skin-side down in the Dutch oven for 4-5 minutes until golden brown, then flip and sear 2-3 minutes more. Transfer to a plate.
Pour the strained chile sauce into the Dutch oven with 1 cup of water, scraping up browned bits. Nestle the chicken skin-side up in the sauce, add bay leaves, bring to a boil, reduce to a simmer, cover, and braise for 1 hour 15 minutes to 1 hour 30 minutes until tender.
Remove chicken and let rest for 5 minutes. Discard bay leaves, taste and adjust seasoning. Remove skin, shred meat with two forks, discard bones, and return chicken to the consomé or keep separate.
Skim fat from the consomé into a skillet. Dip tortillas in the broth and fry in the hot fat with shredded chicken, folding in half. Cook 2-3 minutes per side until crispy. Serve with warm consomé, onion, cilantro, lime, and oregano.