Stir rice and water together in a microwave-safe bowl. Cover and cook in the microwave on high until water is fully absorbed, about 8 minutes. Fluff with a fork; cover and set aside.

Whisk together soy sauce, water, honey, cider vinegar, and cornstarch in a small bowl; set sauce mixture aside.

Heat olive oil in a nonstick skillet over medium heat. Stir in garlic and cook for 10 seconds. Add broccoli, carrots, onion, and black pepper; cook and stir until broccoli and carrots are tender, about 5 minutes. Stir in mushrooms and cook for 2 minutes. Remove vegetables from the skillet and set aside.

Return the skillet to heat and pour in sauce mixture; cook for 1 minute. Add shrimp and stir until shrimp are bright pink on the outside, meat is no longer transparent, and sauce thickens, about 3 minutes. Stir vegetables into the pan and serve over brown rice.