Bring 1 cup soy sauce, ½ cup sugar, and 2 tablespoons mirin to boil in small saucepan over medium-high heat, stirring to dissolve sugar.
Remove from heat and let the teriyaki sauce cool completely.
Peel and thinly slice a 2-inch piece of ginger.
Peel 5 garlic cloves.
Combine ¾ cup teriyaki sauce, ginger, and garlic in blender and process until smooth, about 20 seconds.
Set aside remaining teriyaki sauce for serving (you should have about ½ cup).