In a small mixing bowl, combine the garlic, ginger, brown sugar, honey, white wine, soy sauce, and black pepper. Mix well until all the ingredients combine.
Place shrimp in a medium bowl, add about two tablespoons of the teriyaki mixture, and toss until it completely coats all the shrimp. Let it marinate in the refrigerator for about 15 minutes.
Heat oil in a large skillet over medium-high heat. Then, add the shrimp in a single layer and cook for a minute or two per side until pink.
Remove them from the pan and transfer to a plate. Add the teriyaki sauce to the pan and bring to a boil.
In a small bowl, whisk two tablespoons of water and cornstarch until smooth, and add it to the sauce, stirring until fully combined. Reduce the heat to low and simmer for 3-4 minutes or until the sauce thickens.
Return the shrimp to the pan and stir to coat evenly with the sauce. Cook for about one more minute, being careful not to overcook the shrimp.
Serve over white rice and veggies garnished with green onions and sesame seeds if desired.