The first step of our tarte Tatin recipe was on the stovetop, not in the oven. We arranged apple quarters in concentric circles in a skillet on their cut side so we could fit more fruit, and flipped the apples over as they caramelized. We prepared the caramel right in the skillet with the apples so the flavors melded and the apples were boiled in the buttery caramel sauce until they absorbed the syrup and become virtually candied. We then covered the syrup-soaked apples with an egg pastry that contained confectioners' sugar rather than granulated sugar, which can make the dough grainy. After baking our tarte Tatin recipe, we flipped the tart over, revealing concentric circles of apples glazed with golden caramel.
Note: Be sure to cook the caramel to a rich amber in step 4; otherwise, the apples will look pale and dull rather than shiny and appealingly caramelized.
To Make Ahead: The dough can be wrapped tightly in plastic wrap and refrigerated overnight; let stand at room temperature to warm slightly before rolling it out. The topping can be made 1 day ahead and refrigerated in an airtight container.
1. For the pastry: Pulse flour, confectioners' sugar, and salt in food processor until combined. Scatter butter over dry ingredients; process until mixture resembles cornmeal, 7 to 12 seconds. Turn mixture into medium bowl; add egg and stir with fork until little balls form. Press balls together with back of fork, then gather dough into ball. Wrap dough in plastic, then flatten into 4-inch disk. Refrigerate at least 30 minutes.
2. Unwrap dough and turn out onto well-floured work surface. Sprinkle with additional flour. Starting from center of disk outward, roll dough into 12-inch circle, sprinkling flour underneath to prevent sticking. Slide lightly floured rimless baking sheet or pizza peel under crust, cover with plastic, and refrigerate while preparing apples. Adjust oven rack to upper-middle position and heat oven to 375 degrees.
3. For the apples: Melt butter in 10-inch cast-iron or ovenproof nonstick skillet over medium heat; remove from heat and sprinkle evenly with sugar. Arrange apples in skillet by placing first apple quarter, cut side down and with one end touching skillet wall. As you continue to arrange apples, lift each quarter on its edge while placing next apple quarter on its edge, so that apple quarters stand straight up. Fill skillet middle with remaining quarters, placing them cut side down.
4. Return skillet to high heat; cook until juice turns from butterscotch to rich amber color, 10 to 12 minutes. Remove skillet from heat and, using tip of paring knife or fork, turn apples onto their uncaramelized sides. Return skillet to highest heat; boil to cook uncaramelized sides of apples, about 5 minutes longer.
5. Remove skillet from heat. Slide prepared dough from baking sheet onto apple filling and, taking care not to burn your fingers, tuck dough edges gently up against skillet wall.
6. Bake until crust is golden brown, 25 to 30 minutes. Set skillet on wire rack; cool about 20 minutes. Loosen edges with knife, place serving platter on top of skillet, and, holding platter and skillet together firmly, invert tart onto serving platter. Scrape out any apples that stick to skillet and put them back into place. (The tart can be kept for several hours at room temperature, but make sure to unmold it onto heatproof platter. Before serving, warm tart on platter for 10 minutes in 200-degree oven.)
7. For the topping: Beat heavy cream and sour cream together at medium-high speed in bowl of hand-held mixer until mixture thickens and holds soft but definite peaks. Accompany each wedge of tart with generous dollop of topping.
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