In a large skillet or Dutch oven, heat the olive oil over medium heat. Add the sliced onion and sauté until it becomes translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute, until fragrant.
Next, add the chopped jalapeño and chipotle chiles (along with the adobo sauce) to the skillet. Stir to combine and allow the mixture to cook for another 2-3 minutes, letting the flavors meld together.
Pour in the fire-roasted tomatoes or salsa along with the chicken broth. Stir everything together, ensuring the chipotle chiles are well incorporated into the sauce.
Add the honey, brown sugar, ground cumin, oregano, lime juice, lime zest, and bay leaf to the pot. Season with kosher salt and black pepper to taste. Bring the mixture to a gentle simmer.
Add the chicken breasts to the sauce, ensuring they are submerged. Cover the skillet and let the chicken simmer for about 20-25 minutes, or until fully cooked and tender.
Once the chicken is cooked, remove it from the skillet and shred it using two forks. Return the shredded chicken to the skillet, stirring it into the sauce. Let it simmer for an additional 5 minutes to absorb all the flavors.
Remove the bay leaf before serving. Serve the Chicken Tinga warm, garnished with fresh cilantro, crumbled cotija cheese, lime wedges, pickled red onions, and sliced avocado. Enjoy it in tacos, burritos, or simply on its own!