Combine peanut butter, soy sauce, rice vinegar, chili-garlic sauce, brown sugar, ginger, and 3 tablespoons broth in processor; blend until smooth. Season dressing to taste with salt and pepper. Cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain pasta; rinse with cold water to cool and drain again. Transfer pasta to large bowl. Add chicken, carrots, green onions, bell pepper, and cilantro; toss to blend. Pour dressing over and toss to coat, adding more broth by tablespoonfuls if dressing is too thick. Season salad to taste with salt and pepper.