Place the chicken breasts or thighs in a large pot or Dutch oven. Add the chicken broth, half of the sliced onion, and a pinch of salt. Bring to a boil, then reduce heat, cover, and simmer for 15-20 minutes until cooked through. Remove chicken and shred it using two forks. Reserve the cooking liquid.
While the chicken cooks, prepare the sauce: In a blender, combine the diced tomatoes, tomato sauce, chipotle peppers, adobo sauce, garlic, oregano, and cumin. Blend until smooth.
Heat the olive oil in a large skillet over medium heat. Add the remaining half of the sliced onion and cook until softened, about 5 minutes.
Pour the blended sauce into the skillet. Bring to a simmer and cook for 5 minutes, allowing the flavors to meld.
Add the shredded chicken and 1/2 cup of the reserved chicken cooking liquid to the sauce. Stir well to coat the chicken completely.
Simmer uncovered for 10-15 minutes, stirring occasionally, until the sauce thickens slightly. Taste and adjust salt as needed.
Serve the Chicken Tinga hot over warmed corn tortillas for tacos or on crispy tostada shells. Top with lettuce, queso fresco, and avocado.
Notes
For Slow Cooker: Place raw chicken, sliced onion, broth, tomatoes, tomato sauce, chipotles, garlic, oregano, and cumin in the slow cooker. Cook on low for 6-8 hours or high for 3-4 hours. Shred chicken in the cooker, stir in adobo sauce, and cook for 15 more minutes on high.