In the bowl of a food processor or blender, combine diced onion, chicken broth, chipotle chiles, adobo sauce, garlic, 2 tablespoons cilantro, cumin, oregano and salt. Blend until smooth.
Heat a large cast iron Dutch oven over medium-high heat. Add 1 tablespoon of oil. Cooking in batches, brown chicken for 2-3 minutes per side. Transfer to a plate. Add the other tablespoon of oil to brown the second batch of chicken.
Add the sauce to the pot, scraping any brown bits from the bottom of the pan and bring to a boil. Nestle the chicken pieces into the sauce and reduce heat to a simmer. Cover pot, leaving just a small slit open for excess steam to escape. Cook on low for 40-45 minutes or until chicken is tender and can be shredded. Stir once or twice to make sure nothing is sticking to the bottom of the pot.
While chicken is cooking, make the Cilantro Lime Sour Cream sauce. Combine sour cream, lime juice, cilantro, and salt in a small bowl. Store covered in the fridge until ready to serve.
Remove pot from heat and shred chicken using 2 forks. If the sauce seems too thin, remove the chicken and boil the sauce until it thickens enough to coat the chicken. Return the shredded chicken to sauce and toss to coat.
Serve in warmed tortillas or taco shells with shredded cabbage, fruit salsa, cotija cheese and cilantro lime sour cream sauce.