Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced garlic and ginger, and sauté for about 30 seconds until fragrant.
Add the shrimp to the skillet and cook for 2-3 minutes, until they turn pink and opaque.
Remove the shrimp from the skillet and set aside.
In the same skillet, add the sliced bell pepper, snap peas, and broccoli. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Return the shrimp to the skillet. Add the soy sauce, honey, sesame oil, and the cornstarch mixture. Stir well to combine and cook for an additional 2 minutes until the sauce thickens.
Season with salt and pepper to taste.
Serve over cooked rice or noodles.