Stir brown sugar, corn syrup, and butter together in a small saucepan over low heat until butter is melted and mixture is combined, about 5 minutes.
Add peanut butter, evaporated milk, and marshmallows; cook, stirring constantly, until marshmallows are melted and mixture is smooth, 3 to 5 minutes more.
Stir vanilla into peanut butter mixture, remove from heat, and transfer mixture to a fondue pot.
