Dissolve the cornstarch in 1/2 cup of cold water; set aside.
Whisk together the soy sauce, peanut butter, brown sugar, white vinegar, sesame oil, and 1 cup warm water in a small saucepan over medium heat; simmer and stir until sugar has dissolved. Stir in the cornstarch mixture; simmer until the sauce is thick, 1 or 2 minutes. Serve warm. Garnish with chopped peanuts and mint leaves as desired.