1. With machine on, toss garlic into feed tube of a food processor. Add peanut butter, lime juice, soy sauce, and hot pepper and process until blended. Pour broth through feed tube slowly and process until smooth. Set sauce aside.
2. In a large pot of boiling salted water, cook vermicelli until just tender, 5 to 6 minutes, adding snow peas to water during last 30 seconds of cooking. Drain pasta and snow peas into a colander.
3. While pasta is cooking, heat oil in a wok or large frying pan over high heat. Add chicken and stir-fry 2 minutes. Add bell pepper and stir-fry until chicken is white throughout and pepper is crisp tender, 2 to 3 minutes longer. Remove wok from heat.
4. Add noodles, snow peas, and peanut sauce to wok. Toss gently to combine. Serve noodles with scallions and cilantro sprinkled on top.