In a large pot, add the meat, onion, garlic, carrots, bay leaves, and dried chiles. Cover with 7-8 cups of hot water.
Add chicken bouillon, oregano, cumin, and salt. Stir and bring to a boil.
Boil for 30 minutes, then skim the surface to remove impurities.
Remove softened peppers, onion, garlic, and carrots. Blend until smooth, adding broth as needed for consistency.
If needed, strain the blended mixture back into the pot and season with chili powder.
Cover the pot and simmer for about 3 hours or until meat is fork-tender.
Remove meat and chop into small pieces for tacos.
Heat a griddle on medium. Dip tortillas in reserved grease and warm on griddle.
Top each tortilla with chopped meat and cheese, then fold and cook until crisp and golden on both sides.
Serve tacos with a bowl of the flavorful broth and garnish with diced onions and cilantro.