Tarte tatin can also be made with pears (comice are best, just as they begin to ripen). For the traditional tarte tatin, however, you must use apples, preferably Golden Delicious, which are not good eaten raw but hold their shape nicely in a tart. The tarte tatin is baked upside-down, with the apples under the crust, which, when the finished tart is flipped, becomes the bottom. I peel, core, and quarter four Golden Delicious apples. Then, in the copper tatin pan that I bought from Fred Bridge fifty years ago, I caramelize a half-cup or so of granulated sugar in a quarter-stick of unsalted butter until the sugar becomes the color of honey. Be careful not to cook the caramel for more than a few seconds beyond this stage or the sugar will darken too much. You can move the caramel with a wooden spoon to even the color, which will be a little darker in some places than others. Then turn off the flame and wipe the wooden spoon clean (or the sugar will harden and stick to it).
Carefully, for the caramel is burning hot, lay the apple wedges thick side down in a circle on the caramel, shaping one of the quarters to fill the center of the circle. Use any remaining scraps to fill gaps and sprinkle a good handful of arrowroot over the apples to hold the syrup. Now make a crust of simple pie dough by spinning in a food processor two cups of all-purpose flour with a stick of unsalted butter cut into chunks until the butter is incorporated but still a little lumpy. Then add a half-cup or a little less of ice water, a sprinkle at a time, processing after each addition, until the dough begins to form.
As soon as it forms, remove it from the processor onto a marble slab or plastic sheet, and knead dough into an oblong. You might enclose the dough in plastic wrap at this point and let it rest in the refrigerator for a half hour or so to relax the gluten, or you can skip this step, as I usually do. Then roll out the dough in a circle about an eighth of an inch thick, place the tarte pan with its apples (or pears) adjacent to the dough, roll the dough onto the rolling pin, and place it over the apples, discarding the trimmings or saving them for another purpose. With a fork I tuck the edge of the dough down into the pan. Then I slip the pie onto the middle shelf of an oven just under 360 degrees, at which temperature the fruit will not stick to the pan when you turn it right side up. But if you forget and some of the slices stick, just shove them with a wooden spoon from the pan into the gaps where they belong and smooth everything out. When the crust begins to darken, after about forty minutes, slip the pie out of the oven and let it cool for ten minutes or so.
Then carefully place the plate on which you plan to serve the tarte over the pastry and flip the pie over. If the syrup is too runny, spoon it back over the pie and with a damp paper towel wipe up any excess syrup from the serving plate. A dedicated tarte tatin pan is not essential. A well-seasoned iron skillet or even an eight-inch sauté pan will do just as well. Serve the tarte warm with vanilla ice cream.