In a small bowl, combine 1/4 cup low-sodium soy sauce, 2 tablespoons honey (or sugar), 1 clove minced garlic, 1/2 teaspoon ground ginger, and 1 tablespoon cornstarch. Whisk together until smooth and set aside.
In a wok or large skillet, heat 1 teaspoon of oil over medium-high heat. Ensure the oil is hot before adding the shrimp.
Add the 1 lb of peeled and deveined shrimp to the hot pan. Cook for about 2-3 minutes, stirring frequently, until they turn pink and opaque. Remove the shrimp from the pan and set aside.
In the same pan, add 1/2 cup of water and the 1 cup of blanched broccoli florets. Cover and steam for about 2 minutes until the broccoli is bright green and tender-crisp.
Return the cooked shrimp to the pan with the broccoli. Pour the prepared sauce over the shrimp and broccoli. Stir to coat everything evenly. Continue cooking for another 2 minutes, allowing the sauce to thicken and bubble.
Drizzle with 1 teaspoon of sesame oil, if using, and give everything a final stir. Serve the Quick 10 Minute Shrimp Teriyaki Stir-Fry over steamed white rice or noodles, and enjoy your delicious meal!