Rinse chicken; pat dry. Combine sesame oil and crushed red pepper; brush over chicken.
Grill chicken on the lightly greased rack of an uncovered grill directly over medium heat for 12 to 15 minutes or until tender and no longer pink, turning once.
Meanwhile, for sauce, in a small saucepan,* stir together sugar, peanut butter, soy sauce, oil, garlic, and 2 tablespoons water. Heat on grill rack until sugar is dissolved, stirring frequently. For the last 1 minute of grilling, place split rolls on the grill rack to toast.
To serve, place cooked chicken breasts on bottom halves of rolls; spoon on sauce and top with radish sprouts, broccoli, peanuts (if desired), and roll tops. Makes 4 servings.
*Note: The heat from the grill will blacken the outside of the saucepan, so use an old one or a small cast-iron skillet.