1.2 kilograms cooking apples (about 5), such as Honey Crisp, Spartan or Mutsu
¼ cup + 2 tablespoons unsalted butter, divided
½ cup + 2 tablespoons granulated sugar
1 tablespoon lemon juice
Preheat the oven to 375 degrees Fahrenheit (190 degrees Celsius). On a lightly floured surface, roll the pastry out into a circle and cut it so that it is 9-inches (23 centimetres) across (using the ring of a nine-inch/23 centimetre fluted pan creates a lovely edge to the pastry). Dock this with a fork and chill until ready to use.
Peel the apples, cut them in half and core them. Melt 2 Tbsp (30 grams) of the butter and pour this over the apples, tossing with two tablespoons (25 grams) of the sugar to coat. Set aside.
Place a nine-inch (23 centimetres) skillet (or other round pan that go from the stovetop to the oven) over medium-high heat and stir together the remaining ¼ cup (60 grams) of butter, ½ cup (100 grams) of the sugar and the lemon juice. Once bubbling at the edges, add the apples, arranging them so the curved sides are at the bottom and they are overlapping slightly, to pack them in. Increase the heat to high and cook for two to three minutes, until bubbling vigorously at the edges. Place the pan (without pastry) in the oven to bake for 15 minutes - this allows some of the steam to escape before adding the pastry.
Pull the pan from the oven and place the chilled puff pastry on top of the apples, tucking it in a little around the edges. Return the pan to the oven and bake for 30-35 minutes, until the pastry is a golden brown. Let the tarte cool in the pan for 10-20 minutes so that it is easier to handle. Use a palette knife to loosen any apples that might stick to the sides of the pan. Place a plate larger than the pan over the pan and invert both (use a tea towel). Lift up the pan to reveal the tarte.
Serve slices of the Tarte Tatin warm or at room temperature.