Heat a fondue pot until warm.
Heat the whipping cream in a medium saucepan over low heat until bubbles form along the sides of the pan. Add the chocolate and continue cooking, stirring occasionally, until the chocolate is melted. Stir in the mascarpone cheese and butter. When the mixture is smooth add the rum and vanilla.
Pour into the fondue pot and serve with apples. Adjust the heat to keep the mixture smooth but do not let the chocolate boil.