Heat 1 teaspoon sesame oil in a large nonstick skillet over medium-high heat. Add broccoli, and sauté 4 minutes. Add 1 teaspoon sesame oil, shrimp, and minced garlic, and sauté 4 minutes or until the shrimp are done.
Combine sugar and next 4 ingredients (sugar through chili paste). Add to skillet; cook 1 minute, stirring constantly. Stir in sliced water chestnuts. Serve over rice, and sprinkle with green onions.
Note: You can find red chili paste, which comes in a bottle, in the Asian section of your supermarket.