In a 10-inch oven-proof skillet, sprinkle the sugar evenly over the bottom and drizzle with water. Cook over medium heat, stirring occasionally, until the mixture bubbles and turns light amber, 5 to 7 minutes. Stir in the butter until melted. (It will bubble up so be careful.)
Add the apples. Cook, stirring the apples every few minutes until the caramel is a deep amber color, about 15 minutes. Remove from the heat and arrange the apples, curved side down in concentric circles in the skillet.
Roll out the puff pastry slightly and cut it into an 11-inch circle. Place over the apples, tucking the edges down with a spatula. Place on a rimmed baking sheet.
Bake for 35 to 40 minutes or until the puff pastry is a deep golden brown on top.
Let cool on a wire rack for 15 minutes (up to 30 if using a cast-iron skillet). Carefully invert the tart onto a rimmed serving plate.
Try not to cut the apples too small. Quartering them helps prevent the apples from turning into mush as it cooks with the caramel.
If you don’t have a 9-inch oven-proof skillet, cook the caramel and apples in a skillet and then arrange the apples in a 9-inch round cake pan, pouring any remaining caramel over the top of the fruit before placing the puff pastry.
Make sure the puff pastry has thawed before rolling it out, or it’ll rip.
For extra flavor, you can add a sprinkle of cinnamon or apple pie spice.
Make flipping the Tarte Tatin easier by running a knife around the edge of the crust before flipping.
If the apples shift as you flip the tarte Tatin out of the pan, you should be able to nudge them back in place. Once the dessert is fully cooled, it’ll set, and you won’t be able to fix it, so work quickly!
Apples shrink a lot when they cook, so pack as many in the pan as possible.
Tatins can be made with pears, plums, nectarines, or peaches as well.