Heat a dry skillet over medium heat. Toast the guajillo, ancho, and chipotle chiles for about 30 seconds per side until fragrant — keep them moving so they don't burn. Transfer them to a bowl and cover with boiling water. Let them soak for 20 minutes until soft.
While the chiles soak, char your tomatoes, onion, and garlic in that same dry skillet over medium-high heat for 5–7 minutes, turning occasionally, until they get some nice dark spots.
Drain the soaked chiles and add them to a blender along with the charred tomatoes, onion, and garlic. Pour in 1 cup of chicken broth, the apple cider vinegar, oregano, cumin, cinnamon, cloves, black pepper, and salt. Blend until completely smooth. Strain the sauce through a fine mesh strainer and set aside.
Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season your chicken thighs with salt and pepper, then sear them skin-side down for 4–5 minutes until golden. Flip and cook another 3 minutes. Remove and set aside.
Pour the blended chile sauce into the same pot and cook for 3–4 minutes, stirring frequently. Add the remaining cup of chicken broth and the bay leaves, then nestle the chicken back in. Bring to a boil, then reduce heat to low. Cover and simmer for 1 hour 30 minutes until the chicken is fall-off-the-bone tender.
Remove the chicken from the pot, discard the bones and skin, and shred the meat with two forks. Skim any excess fat off the top of the consomé — but save about ¼ cup of that flavorful fat on the side because you'll need it for frying. Keep the consomé warm for dipping.
Heat a skillet or griddle over medium heat. Dip each corn tortilla in the reserved chile fat to coat both sides, then lay it flat on the skillet. Add a handful of cheese to one half, then pile on some shredded chicken. Fold the tortilla over and cook 2–3 minutes per side until crispy and the cheese has melted.
Plate your tacos with chopped onion, fresh cilantro, lime wedges, and a bowl of hot consomé on the side for dipping. Spoon some salsa verde over the top and enjoy immediately!