Trim ends from green onions; cut off green tops. Cut tops into 2-inch lengths; set aside for serving. Cut white bottoms into 1-inch lengths.
In a 6-to 8-quart Dutch oven cook white parts of green onions and the sweet pepper in hot oil 5 minutes, stirring occasionally. Add the next five ingredients (through crushed red pepper). Cook and stir 30 seconds. Add broth and chicken. Bring to boiling; reduce heat. Simmer, covered, 35 minutes or until chicken is no longer pink (180 degrees F). Remove chicken to a cutting board. Set aside until cool enough to handle.
Add sweet potato and eggplant to the Dutch oven. Bring to boiling; reduce heat. Simmer, covered, 10 to 15 minutes or until potatoes are tender. Meanwhile, ladle about 1/2 cup of the hot broth into a medium bowl. Whisk in peanut butter until smooth. Whisk in tomato paste.
Remove chicken meat from the bones and coarsely shred the chicken using two forks. Add shredded chicken, peanut butter mixture, and tomatoes to the pan. Cook, covered, over medium-low heat 5 minutes, stirring occasionally. Stir in parsley.
Serve stew topped with green onion tops and peanuts.