Place soy sauce, brown sugar, mirin, grated garlic cloves, and ginger paste in a saucepan. Bring to a boil over medium heat, then stir until the sugar is dissolved. In a separate small bowl, whisk together cornstarch and water. Pour the cornstarch slurry into the pan to thicken the sauce.
Bring back up to a boil, then simmer. Remove from the heat and allow to cool completely. Teriyaki sauce can be made up to 1 week in advance.
– Make-ahead, leftovers, and storage: Teriyaki sauce can be stored in an airtight container in the refrigerator. To reheat, simply microwave the sauce on high for 30 seconds or until heated through. Alternatively, you can add teriyaki sauce directly to the pan with veggies, meats, or seafood.