Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat; when hot, season the chicken breasts with salt and pepper and brown 3–4 minutes per side until golden; transfer to a plate and set aside.
In a large Dutch oven, heat the remaining 1 tablespoon olive oil over medium-high heat; add the sliced onion and sauté 4–5 minutes until softened.
Add the minced garlic to the onion and cook about 1 minute until fragrant, stirring frequently.
Remove the pot from heat and transfer the onion–garlic mixture to a blender. Add 2–4 chipotle chiles (to taste) plus 1 tablespoon adobo sauce, chopped jalapeño, the can of fire-roasted tomatoes, chicken broth, honey, brown sugar, cumin, 2 tablespoons chopped cilantro, lime juice, lime zest, and dried oregano.
Cover and purée until smooth, then return the sauce to the Dutch oven.
Add the browned chicken and bay leaf to the sauce, reduce heat to medium-low, and simmer 15–20 minutes until the chicken is cooked through and tender.
Remove and discard the bay leaf, then shred the chicken with two forks (or a hand mixer) and stir the shredded meat into the sauce.
Simmer the shredded chicken in the sauce 10 more minutes to meld flavors; taste and adjust salt, pepper, or chipotle heat if needed.
Serve the chicken tinga warm with tortillas and desired toppings such as chopped cilantro, cotija cheese, lime wedges, pickled red onions, salsa, sliced avocado, and extra chopped jalapeños.