Whisk together brown sugar, vinegar, mint and vanilla in a large bowl until brown sugar is dissolved. Add peaches and toss gently to combine. Let stand for at least 5 minutes or up to 30 minutes. Meanwhile, beat cream until soft peaks form. Gradually beat in icing sugar until stiff; refrigerate.
Cut cake into 8 slices. Spread butter evenly over both sides of cake slices.
Grill cake slices over medium heat on natural gas barbecue, turning once, until lightly browned.
To serve, place cake slices on individual dessert plates. Spoon peach mixture over cake slices. Top with whipped cream.
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