Teriyaki Sauce: Heat a large 12-inch skillet over medium heat on the stovetop. To the pan add water, soy sauce, brown sugar, rice vinegar, honey, garlic, ginger, sesame oil, salt, and black pepper.
Whisk to combine then increase heat to medium-high and bring to a boil. In a small bowl, whisk together cornstarch and water until dissolved.
Whisk the cornstarch slurry into the sauce, mixing until well combined. The sauce will begin to thicken in 1-2 minutes. Remove the sauce from the heat. Set aside to cool. (You can do this up to 2 days in advance and store chilled until making the stir fry).
Shrimp: Pat dry the shrimp with a paper towel, and season with 1/2 tsp salt and 1/2 tsp black pepper. Cook the shrimp over medium-high heat in two tablespoons of oil for 2-3 minutes. Use a slotted spoon to transfer to a plate.
To the skillet add reserved vegetable oil and sesame oil. Add snow peas, bell peppers, and onion. Season with 1/2 tsp salt and 1/2 tsp pepper. Cook the vegetables for 3-5 minutes or just until crisp-tender.
Add the shrimp back to the skillet and pour the teriyaki sauce over the shrimp and vegetables tossing to coat. Cook over medium heat just until the shrimp are warmed through.
Garnish with sesame seeds and green onions. Serve immediately over cooked white rice or fried rice.