Cook the rice according to the package directions. In a small bowl, whisk together the soy sauce, honey, cornstarch, garlic, and ½ cup water.
Season the shrimp with ¼ teaspoon each salt and pepper. Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the shrimp and cook, tossing occasionally, until almost opaque throughout, 2 to 4 minutes; transfer to a plate.
Add the remaining tablespoon of oil to the skillet. Add the carrots, broccoli, and onion and cook, tossing, until beginning to soften, 3 to 5 minutes.
Return the shrimp to the skillet, whisk the soy sauce mixture again to redistribute the cornstarch, and add it to the skillet. Cook, tossing frequently, until the shrimp are opaque throughout and the sauce is thickened, 1 to 2 minutes more. Serve with the rice.