Cook noodles in boiling water 6 minutes. Rinse and drain. Keep warm.
Place 1/2 cup peanuts in a food processor; process until smooth (about 2 minutes), scraping sides of bowl once.
Combine peanut butter, broth, and next 5 ingredients (broth through garlic) in a large skillet; bring to a boil. Reduce heat; simmer 1 minute. Pour broth mixture into a blender or food processor; let stand 5 minutes. Process until smooth. Stir in vinegar.
Cook shrimp in boiling water 2 minutes or until done; drain.
Combine noodles, shrimp, bell pepper, cucumber, onions, and basil in a large bowl. Add peanut sauce; toss gently to coat. Sprinkle with chopped nuts; serve with lime wedges.