To prepare saté, place first 13 ingredients in a food processor, and process until smooth. Place shallot mixture and chicken in a large zip-top plastic bag; seal and marinate in refrigerator 10 minutes.
To prepare peanut sauce, combine peanut butter and next 6 ingredients (through Sriracha) in a medium bowl; stir well with a whisk.
Remove chicken from bag; discard marinade. Thread chicken on 8 (12-inch) wooden skewers. Place skewers on the rack of a broiler or roasting pan coated with cooking spray. Broil 12 minutes or until done. Serve with peanut sauce.