How to Make It
Preheat the oven to 400°. In a small saucepan, combine the sugar, water and corn syrup and bring to a simmer over moderate heat. Simmer without stirring until an amber caramel forms, about 6 minutes. Pour the caramel into an 8-inch ovenproof skillet, tilting to coat the bottom. Set the peach halves in the caramel, cut sides up.
On a lightly floured surface, cut the puff pastry into an 8-inch round. Set the round over the peaches in the skillet and bake until the pastry is richly browned and puffed, about 28 minutes. Remove the skillet from the oven and let stand for 5 minutes. Carefully invert the peach tart onto a cake plate and let cool slightly. Cut the tart into wedges and serve with vanilla ice cream.