Season chicken thighs generously with salt and pepper. In a large Dutch oven or soup pot, heat olive oil over medium-high heat. Add chicken, skin-side down, and sear until golden brown, about 5-6 minutes per side. Remove chicken and set aside.
In the same pot with the chicken drippings, add onions and sauté until translucent, about 3-4 minutes. Add garlic and ginger, cooking for another minute until fragrant.
Add carrots, celery, and bell pepper to the pot. Cook for 5 minutes, stirring occasionally. If your vegetables are looking dry, add a splash of broth.
Add jalapeños and all dry spices (cumin, paprika, cayenne, oregano). Stir continuously for 1-2 minutes until spices become fragrant.
Return the chicken to the pot. Add diced tomatoes with their juice, chicken broth, and apple cider vinegar. Bring to a boil, then reduce heat to maintain a gentle simmer. Cover partially and cook for 30-40 minutes until chicken is falling-off-the-bone tender.
Remove chicken pieces and place on a cutting board. When cool enough to handle, remove skin and bones, then shred the meat into bite-sized pieces.
Return shredded chicken to the pot, taste, and adjust seasonings. Allow to simmer for an additional 5 minutes to marry flavors.
Stir in fresh cilantro just before serving. Serve in warm bowls with lime wedges on the side.