Preheat the oven to 400°F (200°C)

Cut the peaches in half and remove the pits. Set aside.

Make the caramel: In a saucepan over medium/low heat, combine sugar and water. Allow the sugar to dissolve first before simmering. Once the sugar is dissolved let the sugar melt and turn a dark amber color without stirring (about 7-10 minutes). Lastly, stir in butter.

Pour the caramel evenly into a 12-cup muffin tin.

Place peach halves cut side down on top of the caramel, prick the peaches all over with a knife, cover with foil, and place in the oven.

After 30 minutes, remove the foil and continue baking for another 30 minutes.

When peaches are done baking, cut the puff pastry into 3-inch rounds and cover each peach half, pressing onto the tin to seal the dough.

Return the muffin tin to the oven and bake until the puff pastry is puffed and golden — about 20 minutes.

Let the tarte tatin rest for 15 minutes before inverting into a serving dish. Serve warm with vanilla ice cream.