Heat olive oil in a large skillet over medium heat. Add onion and sauté until softened. Add garlic and cook 1 minute.
Stir in oregano, paprika, black pepper, cinnamon, cumin, and salt. Toast spices for 1 minute.
Add guajillo chiles, chiles de árbol, tomatoes, apple cider vinegar, honey, bay leaves, and chicken broth.
Bring to a simmer and cook 10–15 minutes until dried chiles are very soft.
Remove and discard bay leaves. Transfer mixture to a blender and blend until smooth. Taste and adjust salt or sweetness.
Add shredded chicken to the skillet over low-medium heat and pour half of the sauce over it. Warm through. Reserve remaining sauce for dipping and brushing tortillas.
Heat a skillet over medium-low. Lightly brush a tortilla with reserved sauce and place sauce-side down in the pan.
Add cheese and sauced chicken, fold, and toast until crispy on both sides.
Repeat with remaining tortillas. Serve with pico de gallo, cilantro, lime wedges, and extra sauce for dipping.