In a large skillet or wok, heat the vegetable oil over medium-high heat.
Add the minced garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the shrimp to the skillet and cook for 2-3 minutes, or until they turn pink and opaque.
Remove the shrimp from the skillet and set aside.
In the same skillet, add the bell pepper, snap peas, and broccoli. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Return the shrimp to the skillet. Add the soy sauce, honey, and sesame oil, stirring to combine.
Pour in the cornstarch mixture and cook for an additional 1-2 minutes until the sauce thickens.
Serve over cooked rice or noodles.