Combine the first 6 ingredients in a medium bowl; cover and chill for 1 hour.
Combine water and next 4 ingredients (water through salt) in a small bowl; set aside.
Heat oil in a stir-fry pan or wok over medium-high heat. Add broccoli; stir-fry 2 minutes. Add shrimp mixture; stir-fry 5 minutes or until shrimp are done. Add cornstarch mixture, and bring to a boil. Cook 1 minute or until sauce thickens. Serve over soba noodles.