For the Chicken Soup: Place chicken pieces and backbone in large Dutch oven or large soup pot. Add onion, pepper, garlic, sour orange, culantro, and mint. Cover with water; stir in salt and black pepper. Bring to a boil over high heat. Reduce heat to medium and simmer, skimming surface occasionally, until chicken is cooked through, about 15 minutes. Using a slotted spoon, transfer chicken pieces to large plate. When cool enough to handle, use paper towels to remove chicken skin; discard. Shred chicken finely. Strain broth into a large bowl. Discard solids and return broth to Dutch oven.

For the Chicken Meatballs: In the bowl of a food processor, pulse onion, bell pepper, and garlic cloves until mixture is a fine paste, 15 to 20 one-second pulses. In a large skillet, melt butter over medium heat. Add onion mixture and annatto and cook, stirring occasionally, until most of the liquid has evaporated and mixture has cooked down into a thick paste, 5 to 7 minutes. Transfer to a large bowl.

Add corn masa mix, 1 teaspoon salt, 1 ½ cups (355ml) strained broth, culantro, mint, sour orange juice, and half the shredded chicken. Stir until thoroughly combined. To test seasoning, form a single ½-inch ball of dough. Bring broth to simmer over medium-low heat. Cook dumpling until it floats to surface, 4 to 5 minutes. Taste and add additional salt to masa mixture if needed.

Using lightly oiled hands, shape dough into 1 ½–inch balls (you should have about 30). Working in 2 batches, add shaped meatballs to simmering broth. Cook until meatballs float to surface, about 8 minutes. Transfer cooked meatballs to a plate, then repeat with remaining meatballs, setting all cooked meatballs on plate as they are ready. Add remaining shredded chicken to broth to heat through, about 1 minute. If serving immediately, divide meatballs between bowls (about 4 meatballs per bowl) and ladle broth over. Serve, garnished with herbs.