prepare the puff pastry
Take the puff pastry from the fridge. Place the pastry over a sheet of parchment paper, then place a 26 cm (10 1/2 - inch) plate in the center of the pastry, making sure it covers the pastry completely. Using a knife, cut out a circle in the size of the plate. Remove the leftover puff pastry. Brush the circle with melted butter and prick it all over with a fork. Transfer the prepared pastry with the parchment paper to a baking sheet and place it in the fridge or even better, in a freezer until needed.TipFeel free to use frozen puff pastry. In that case, roll it to a 2-3mm (1/8 -inch) thickness before using. Always keep your puff pastry cold.
prepare the apples
Peel the apples, cut in half, then remove the core using a teaspoon or a melon baller. Drizzle with lemon juice. Place a 24 cm (9 1/2 - inch) oven-safe skillet over medium heat. Add the sugar and cook for about 6 - 8 minutes, or until the sugar dissolves and the caramel is beautifully golden brown. Don't stir the sugar, but feel free to shake the saucepan in a circular motion from time to time to evenly distribute the sugar. Remove from the heat, and add small cubes of butter. Using a heat-proof rubber spatula, stir vigorously until the butter melts, then place back over medium-low heat. Add the vanilla paste, pinch of salt, cinnamon stick, allspice, and cloves. Stir and add the apples. Cook for about 8 - 10 minutes in the caramel, turning the apples occasionally so that they bathe in the caramel. Remove from the heat and set aside for 8 - 10 minutes for the apples to cool slightly.
bake the tarte tatin
Arrange the apples tightly together against each other in the skillet, making sure the cut-side of the apples is looking up. Take the prepared puff pastry from the fridge or freezer and place it on top. Tuck the pastry down the sides of the pan. Transfer the skillet with the Tarte Tatin into the preheated oven on the middle rack. Bake for 30 - 35 minutes at 200 °C / 390 °F or at 190 °C / 375 °F if you are using a convection oven. Bake until the pastry is beautifully golden-brown and baked.
Remove the baked Apple Tarte Tatin from the oven. Leave in a skillet for one hour to cool. Place a large plate on top of the skillet and carefully pour the leftover caramel from the Tarte Tatin into a small bowl. Then place a large serving plate on top of the puff pastry and invert. Carefully remove the skillet, cut in six equal slices, and serve with vanilla ice cream or whipped cream and some of that preserved caramel from baking.