Heat a Dutch oven or large stockpot over medium-high heat. Add the dried chilies and toast on each side for about 2 minutes. Remove and set aside. Add the oil to the pan. Add the onion and cook for about 5 minutes until beginning to brown. Add the whole garlic cloves and cook for 1-2 minutes until fragrant. Stir in the cilantro, bay leaves, and oregano. Cook for 1 minute.
Add the dried chilies back to the pot. Then add the chicken thighs. Pour in half the chicken broth and bring everything to a simmer. Cover and simmer for 45-60 minutes. If using boneless, skinless chicken breasts remove them as soon as they are cooked through (about 10-15 minutes) so they don't overcook.
Use an immersion blender to blend the broth, chilies, onions, garlic, cilantro, and spices. Alternatively, blend carefully in a blender until smooth. Add the remaining chicken broth. Taste and season with salt as needed.