1. Whisk together soy sauce, water, honey, michiu, and cornstarch in a small bowl; set sauce mixture aside.
2. Heat sesame oil in a nonstick skillet over medium heat. Stir in garlic and cook for 10 seconds.
3. Add broccoli, cauliflower, snow peas, water chestnuts, carrots, onion, and black pepper; cook and stir until broccoli and carrots are tender, about 5 minutes.
4. Stir in mushrooms and cook for 2 minutes. Remove vegetables from the skillet and set aside.
5. Return the skillet to heat and pour in sauce mixture; cook for 1 minute.
6. Add shrimp and stir until shrimp are bright pink on the outside, meat is no longer transparent, and sauce thickens, about 3 minutes.
7. Stir vegetables into the pan and serve over rice.