Place chicken in a pot and add 8 cups water, or enough to cover; bring to a boil. Reduce heat to a simmer and cook until chicken is no longer pink in the center and the juices run clear, about 10 minutes. Remove chicken to a plate.

Transfer cooking liquid and more water (enough so total liquid measures 10 cups) to a 6-quart Dutch oven. Add tomato paste, onion, bouillon cubes, chili powder, and garlic. Cook over medium-high heat until onion is translucent and liquid is almost boiling, 5 to 10 minutes.

Meanwhile, cut chicken into bite-sized cubes. Grind enough chicken in a food processor to get 3 cups. Set aside ground chicken, and add remaining chicken cubes to the soup.

Prepare dumplings: Ladle out a small amount of soup and let cool for a few minutes. Combine ground chicken, masa, all-purpose flour, parsley, chili powder, cumin, salt, and pepper in a bowl. Add a small amount of cooled soup at a time and mix by hand to form a soft dough. (You can also mix in a food processor.)