Special equipment: 8 to 8 1/2-inches ovenproof saucepan or cast iron skillet
Make the Soured Cream Shortcrust Pastry, recipe follows and allow to chill.
Preheat the oven to 400 degrees F.
To prepare the apples: Peel the apples with a vegetable peeler to keep them in a nice rounded shape, and then cut into quarters. Remove the core from each quarter, and set aside. Don't worry if they go brown, and don't cover in water or they will be too wet.
Place the sugar and water in an ovenproof saucepan set over a low-medium heat, and stir until the sugar dissolves. Increase the heat, and boil the syrup until it starts to caramelize around the edges, about 5 minutes. Do not stir once it has come to the boil, otherwise the syrup will crystallize. Once the syrup starts to turn golden, you may need to swirl the pan slightly to even out the caramelization.
Once the syrup is golden caramel in color, add the butter, and swirl the pan again to distribute it throughout the caramel.
Remove the pan from the heat, and arrange the apple quarters in a concentric circle around the outside of the pan, and any remaining pieces in the center, keeping in mind that the tart will be flipped over when serving. The apples must completely cover the base of the pan; you may need an extra apple!
Place the pan back over a medium heat, and cook for 10 minutes, to slightly caramelize the apples, while you roll out the pastry.
On a lightly floured work surface, roll the pastry out to a round about 3/4-inch wider in diameter than the pan. Remove the pan from the heat, and place the pastry on top of the almost cooked apples. Using the base of a spoon or a fork, tuck the pastry in around the edges of the apples. Brush the pastry with the beaten egg, and then using a skewer or fork, prick a few holes in the pastry.
Bake in the oven for 25 minutes or until the pastry is golden and the apples feel cooked when you insert a skewer through the center.
Remove from the oven and allow to stand for just a few minutes before placing a plate on top of the pan and carefully (it is hot!) but quickly flipping it out. Use a plate with a slight lip to catch the delicious juices. Cut into slices to serve. Serve with whipped cream, ice cream or whipped cream with a little icing sugar and cinnamon or Calvados mixed in.
Place the flour, salt, and butter in a food processor and whiz or pulse briefly. Add half the sour cream and continue to whiz. You might add a little more sour cream, but not too much as the mixture should be just moist enough to come together.
If making by hand, rub the butter into the flour until it resembles coarse bread crumbs. Then, using your hands, add just enough egg to bring the dough together. With your hands, flatten out the ball of dough, until it is about 3/4-inch thick, and then wrap in plastic wrap or place in a plastic bag and leave in the refrigerator for at least 30 minutes or, if you are pushed for time, in the freezer for 10 to 15 minutes.
Makes 1 crust (about 14 ounces).
Variations: Pear and ginger tarte tatin: Use 4 to 5 pears of medium ripeness, instead of the apples and add 1 teaspoon of grated fresh ginger root in with the butter. Add 1 teaspoon of ground cinnamon to the pastry. You can also make this with puff or sweet shortcrust pastry. If you wish, use golden caster or granulated sugar, but it is a little trickier to see when it is caramelized, so keep watching the pan. The mixture will go a shade darker than the original golden color and should take about 5 minutes in total over a medium-high heat. If it burns, I would suggest cutting your losses and starting again!