Sauté celery and onion in butter in a large Dutch oven over low heat 10 minutes or until tender. Remove from heat.
Add flour, stirring until smooth; stir in broth. Place over medium heat, and bring to a boil, stirring constantly. Add peanut butter, beating with a wire whisk until blended. Reduce heat; cover and simmer 15 minutes. Stir in half-and-half and pepper; heat just to boiling.
Ladle soup into individual serving bowls; garnish with chopped peanuts. Serve immediately.