Whisk together the soy sauce, honey, brown sugar, rice vinegar, cornstarch, and crushed red pepper flakes (if using), in a small liquid measuring cup or bowl. Set aside.
Heat the vegetable oil and sesame oil in a large skillet over medium heat. Add the garlic and ginger and cook until fragrant, about 30 seconds.
Add the shrimp and soy sauce mixture and cook until the shrimp turn pink and the sauce is thickened, about 3 to 4 minutes. (Add a little water, 1 tablespoon at a time if the sauce gets too thick before the shrimp are cooked.)
Stir in the green onions and sesame seeds and serve with hot-cooked white rice.