Place the chicken thighs, the roughly cut onion, the 4 cloves of pressed garlic, and 1 teaspoon Kosher salt in a large skillet; add just enough water to cover the chicken.
Bring to a boil, then reduce heat to a simmer. Cover and simmer 20 to 25 minutes until the chicken is cooked through.
Use a slotted spoon to transfer the chicken to a platter and let cool until safe to handle. Remove and reserve 1 cup of the poaching broth by straining the pan liquid through a colander into a heatproof bowl; save remaining broth for another use.
Remove skin and bones from the cooled chicken and roughly shred the meat with your fingers or two forks; set shredded chicken aside.
In the same large skillet, heat 1 tablespoon olive oil over medium heat. Add 1 cup chopped onion and cook until soft, about 4 to 5 minutes. Add 3 minced garlic cloves and cook, stirring, about 30 seconds.
Stir in 1 teaspoon dried oregano and 1/2 teaspoon ground cumin and cook, stirring, about 1 minute to bloom the spices.
Add the 14.5-oz can fire-roasted diced tomatoes (with juices), 1 cup reserved chicken broth, 2 tablespoons chopped chipotle peppers, 2 tablespoons adobo sauce, 1 teaspoon Kosher salt, and 2 bay leaves. Stir to combine and simmer about 15 minutes.
Remove and discard the bay leaves. Carefully transfer the sauce to a blender and purée until smooth, about 1 minute, then return the puréed sauce to the skillet.
Stir the shredded chicken into the sauce and cook, stirring often, until heated through, about 5 minutes.
Serve immediately with warmed tortillas and optional toppings: Cotija cheese, chopped cilantro, chopped red onion, and hot sauce.
