Place the flour and salt in a food processor and pulse to mix. Add the fat and pulse until it becomes granular, then dump the mixture into a bowl. Add 2 tablespoons of cold water and mix with a fork. Squeeze some of the mixture between your fingertips. If it holds together, it’s fine; if not, add a little more cold water, but don't add too much or your pastry will shrink during baking. Mix with your hands until the dough comes together, this takes a minute or two. Form the dough into a disk, wrap in plastic, and refrigerate while you tend to the apples.
Peel and halve the apples lengthwise. Remove the core with a melon baller and trim out the rest of the core with a knife.
Melt the butter in a 9-inch cast-iron skillet over medium heat. When the butter has melted, sprinkle the sugar over the top, then nestle the apples in the sugar, cut side up. They should fit snugly alongside one another. (You must pack the apples into the pan because they shrink as they cook.) The sugar and butter should bubble up around the apples. Continue to cook, without stirring, for 30 to 45 minutes, until the caramel is well colored and the apples are soft. Shake the pan from time to time to detach the apples from the bottom and to ensure the caramel cooks evenly, but do not stir. (As I am type A and like to fiddle, I carefully reverse the apples in the caramel so the half that has been sitting out of the pan is submerged.) Cook until the caramel is well colored and the apples are soft when you prod them with a spoon.
While the apples are cooking, roll the pastry into a circle a smidge bigger than the diameter of the frying pan. Cover and refrigerate it.
Crank the oven to 425°F (220°C).
Now you must be patient as the apples slouch into their caramely, buttery bath. When they’re ready, remove the pan from the heat and place it on a baking sheet so it'll be easier to maneuver in and out of the oven. Take the pastry disk from the refrigerator. Wait until the caramel stops bubbling, and then place the pastry on top, pushing down on the edges to cover the apples and tuck it inside the rim of the pan.
Place the pan in the oven and bake about 25 minutes, or until the pastry is nicely browned. Remove the pan from the baking sheet and place it on a cooling rack. Run a knife around the edge of the pan to detach the pastry and the apples from the sides and then leave for 10 minutes (but no more than 10 minutes). To pass the time, line a flat baking sheet with parchment paper.
Now don't think too much about the next step--just do it. Place the parchment-lined baking sheet, paper side down, on top of the frying pan. Flip the frying pan over onto the baking sheet and then use the pan to center the tart on the paper. Slowly lift the frying pan off the tart.
Usually, all the apples drop onto the pastry, if not, you can place them and scrape any remaining caramel from the pan onto the tart. I like to scoop up the extra caramel from the parchment paper and place it back onto the tart. [Editor’s Note: We like to scoop up the extra caramel from the parchment paper and nibble it as we stand back and admire the tart.] Let the tart cool to room temperature and serve with whipped cream.