Dissolve cornstarch in cold water.

Whisk warm water, peanut butter, soy sauce, brown sugar, vinegar, and sesame oil together in a small saucepan over medium heat. Bring to a simmer, then cook, whisking constantly, until sugar has dissolved, 1 to 2 minutes. Stir in the cornstarch mixture and simmer until thick, 1 to 2 minutes.

Spoon sauce into a serving bowl and garnish with peanuts and mint. Serve warm.