Make the chicken: Add the chicken, onion, garlic, bay leaf, and salt to a large saute pan or Dutch oven. Cover the chicken completely with water, plus an additional inch. Bring to a boil, reduce heat to simmer, cover, and cook for 15-20 minutes until the chicken is cooked through and the internal temperature reaches 165˚F.
Reserve 1 cup of the broth and set aside. Transfer the chicken to a cutting board and let it rest until cool enough to handle, about 5 minutes. Shred the chicken with 2 forks, your hands, or mix it in a stand mixer using the paddle attachment and set aside.
Make the sauce: Spray a large baking sheet with nonstick cooking spray or grease with oil. Place the tomatoes and the onion halves on the baking sheet and place under the broiler. Broil on high for 10 minutes, flipping over halfway through, until blackened and charred in some spots.
Add the roasted tomatoes, onion halves, chipotle peppers, garlic, oregano, salt, cumin, and ½ cup of the reserved broth into a blender or food processor. Blend until smooth.
Heat the olive oil in a large saute pan or Dutch oven over medium-high heat. Add the tinga sauce, cover, and cook for 10 minutes, stirring occasionally.
Combine: Add the shredded chicken and stir to combine to evenly coat the chicken. Cook for an additional 10 minutes while the sauce thickens and reduces. If the sauce reduces too much, stir in a splash or two of the remaining reserved broth.
Serve the tinga in warm corn or flour tortillas with cotija cheese, onion, cilantro, and diced avocado.
Notes
Chicken: You can use 4 cups of shredded chicken instead of making it from scratch. Shredding a store-bought rotisserie chicken is a great option, or you can use any leftover chicken you have in the fridge. If using shredded chicken, you’ll need about ½ cup chicken broth.
Chipotles: This recipe has a mild spice level. For more spice, add 2 tablespoons of chipotle peppers.
Tomatoes: To save even more time, you can use 1 (15-ounce) can of fire-roasted diced tomatoes instead of roasting from fresh.
Mexican oregano: If you don't have this, you can use regular oregano instead.
To make this in the slow cooker: Make the sauce as instructed, except use ½ cup of water instead of chicken broth. Then, add the chicken to the slow cooker, pour the sauce on top, cover it, and slow cook on low for 5-6 hours or on high for 3 hours. Shred the chicken, stir it into the sauce, and serve.
To make this in the Instant Pot: Make the sauce as instructed, except use ½ cup of water instead of chicken broth. Then add the chicken to the Instant Pot, pour the sauce on top, and cover. Set the pressure valve to the seal position, turn on Manual or High Pressure, and pressure cook for 10 minutes. Quick release the pressure, carefully shred the chicken, stir it into the sauce, and serve.