Trim away excess skin and fat from chicken. Heat 1 tablespoon olive oil in large dutch oven or stovetop-safe slow cooker insert over medium heat on stovetop. Add chicken and lightly brown on both sides – the amount of time isn’t important, but target about 10 minutes. Remove chicken to plate and set aside. (If you have lots of chicken thighs or a small pan, you may need to brown the chicken in batches - just remove browned thighs to a plate and carry on until you have them all browned.)
Add a fresh tablespoon of olive oil to pan, add onions and red bell pepper strips, cook until softened, about 5 minutes. Add the browned chicken and any accumulated juices to the veggies. Add seasonings and chicken broth. Transfer insert to slow cooker, cover and cook on low heat setting for 4 hours. (If using a dutch oven, lid on and simmer gently on stovetop, 30 – 40 minutes.)When chicken is cooked and falling off the bone, transfer chicken pieces to a cutting board using a slotted spoon. Let sit until cool enough to handle.
Return the dutch oven or slow cooker insert to the stovetop, and boil the remaining liquid to reduce slightly and concentrate the flavors.Remove and discard the skin and bone from each piece of chicken. Chop or shred the meat, return it to the sauce, and you’re ready to serve.