Bring the water and garlic to a boil in a saucepan over high heat. Stir in the edamame, and cook until the edamame are hot, and the liquid has nearly evaporated, about 5 minutes. Reduce the heat to medium-high and stir in the teriyaki sauce, brown sugar, vinegar, and sesame oil. Stir constantly until the sauce has thickened and coats the edamame, about 4 minutes. Sprinkle with sesame seeds to serve.