Bring 2 1/2 cups chicken broth to a boil over high heat.
While the broth is boiling, toast the chili peppers in a hot pan until soft and pliable but not burnt. Transfer to a bowl and add 2 1/2 cups chicken broth, cover and set aside for 30 minutes.
Heat a large heavy bottom oven-safe pot over high heat. When hot, add half of the oil and half of the pork. Season with about 1/2 teaspoon salt and sear, turning to brown the meat on all sides. Transfer to a plate and repeat with the remaining oil and pork. Note that the meat won’t be fully cooked at this point. Transfer the second batch to the plate and set aside. Do not clean the pan.
Add the garlic and cook, stirring, until fragrant, about 1 minute more. Add the tomato paste, if using and cook for 1 minute more, stirring constantly. Add the coconut aminos, fish sauce, bay leaves, cumin, and oregano. Add in all remaining broth and stir until combined. Add back the pork and any juices that have accumulated. Stir in the remaining teaspoon salt. Bring to a simmer.
While the soup comes to a simmer, blend the chili peppers. Transfer the chili peppers and their soaking liquid to a blender and blend on high. Strain this mixture through a fine mesh sieve and into the simmering soup, discarding anything caught in the strainer.
Cover and simmer on low for 3 hours, or until tender when tested with a fork. You can also bake this covered in the oven at 325ºF until tender, about 3 hours, adding water or more stock as needed if the liquid reduces significantly.
Taste and adjust seasoning with salt, as desired. Serve with desired garnishes.