Preheat oven to 375 degrees. In a medium ovenproof nonstick skillet combine sugar, vinegar and water. Cook without stirring until the syrup is become golden. Add butter and vanilla extract, mix well. Arrange pears, cut side up and overlapping, in circle in skillet. Reduce heat to medium-low and cook until pears are tender, 10-15 min. Bake tart until pastry is puffed and golden, about 35 minutes. On a lightly floured surface, roll puff pastry; using a plate about 2 inches bigger then a skillet for the tart, cut out a round. Drap pastry round over pears, tucking edge under
Bake tart until pastry is puffed and golden, about 30-35 minutes. Meanwhile in a medium bowl beat together heavy whipping cream, mascarpone, rum and confectioners sugar. Serve warm tart with a scoop of light mascarpone cream, sprinkle with cinnamon.