I wrote up this recipe at the end of filming for inclusion in the cast and crew cookbook that was compiled as a gift to everyone and distributed at the wrap party. It may seem long, but I am including a lot of detail on technique so you won't make any wrong turns in the recipe.
Making a good tarte tatin is all in the technique. The ingredients are simple--apples, butter, and sugar--but the trick is to get a good dark caramel color and flavor into the apples without overcooking them into a mush. Use your favorite all-butter piecrust recipe (or Julia's Påte Brisée), or use all-butter frozen puff pastry (like Dufour's).
• 6 to 8 Granny Smith apples
• 3/4 cups sugar
• 2 to 3 tablespoons water
• 4 Tablespoons (2 oz.) cold unsalted butter, cut up
• Chilled pastry dough
Choose a pan: a copper tarte tatin mold will be perfect (here's a link to a good one), but you can also use an iron skillet (as long as it doesn't smell like salmon or something) or even a heavy stainless steel (like All-Clad) or non-stick sauté pan. Whatever you choose, it should be about 10" across at the top and have an ovenproof handle.
Peel the apples, quarter them, and cut the cores out. Squeeze half a lemon over them if not using right away.
Preheat the oven to 400 degrees. Pour the sugar into the pan and set over medium heat. Add the water, just enough to be absorbed by the sugar. It's OK to stir it once, to combine the water and sugar, but don't stir it after that. Use a pastry brush dipped in water to make sure there are no sugar crystals clinging to the edges of the pan. Brush periodically during cooking.
Have the cold butter ready by the stove. Cook the sugar over medium to medium-high heat, gently swirling the pan to keep it cooking evenly, until it turns a medium-dark amber color. This will happen very quickly, be careful not to burn it. Keep the heat low if you are unsure once it starts to turn color. If you are using a dark skillet, drop a little of the sugar on a piece of white paper, or paper towel to check the color as it will be hard to judge in the pan. The very moment it looks dark enough, remove the pan from the heat and gently add the cold butter. Don't splash, as the sugar is very hot. It will bubble up a bit.
Off the heat, add the apples, rounded sides down, in concentric circles, starting on the outside edge of the pan. Try to keep the apples somewhat vertical, and pack them as closely as possible. Don't let your fingers touch the hot caramel. Slice any remaining apples into small wedges and scatter them around, filling any holes or low spots.
Return the pan to the stove, and cook the apple mixture, undisturbed, until the apples are softened, and the caramel liquid is starting to thicken. This will take about 15 to 20 minutes, but use your judgment, because much depends on the pan you are using and the heat level. At this point, you can set the apples aside and let them cool a bit. This makes it easier to cover it with pastry, and also helps prevent overcooking the apples, but you can continue with the recipe if you want.
Roll the chilled pastry out until it is 1 to 2 inches larger than the pan you are using. If you are using frozen puff pastry, it will already be flat, but you will need to roll it a little bit so it's big enough. Place the rolled dough on top of the apples, and tuck it in around the apples. Cut a small vent in the center, place on a baking sheet to catch any drips, and place in the lower third of the oven. Bake for 25 to 30 minutes, or until the pastry is nicely browned and the caramel is bubbling up around the edges.
Let cool slightly, at least 10 minutes, or until you are ready to serve the tart. If it has completely cooled before you serve, place it over a low heat for a minute or so to re-melt the caramel. Run a butter knife around the edges to loosen them, and then place a flat plate on top of the tart. Holding the two firmly together (wear oven mitts if it's hot), quickly and carefully flip the unit over and place on the counter. Remove the pan. If any apples stick to the pan, just replace them where they should go on the tart. Serve warm, with crème fråiche, if desired.