THE UPSIDE-DOWN tarte tatin is as emblematic to the French as apple pie is to Americans. Many variations have evolved from this classic, but what remains as the most important factors are the choice of apple and the degree of darkness of the caramel. For this rendition, we cook New York’s Hudson Valley Honeycrisp and serve alongside the tart raw Granny Smith. A crunchy Breton shortbread supports the apple mille-feuille, with paper-thin layers of apple confit topped with beads of Calvados cream.
    Vanilla Sablé Breton
    Croustillant Tuile (makes extra)
    Baked Apple Confit
    Confit Honeycrisp Ice Cream
    Calvados Cream
    Green Apple Sauce
    For the Vanilla Sablé Breton
    1. Preheat the oven to 350°F. Unwrap the dough and place it on a sheet of parchment paper on a flat surface. Top with another sheet of parchment and roll into a ¼-inch-thick rectangular sheet. Slide the dough with the paper onto a baking sheet and remove the top layer of paper. Bake for 8 minutes, or until the edges begin to color. Using the aid of a ruler, cut the hot dough into at least four 3½ × ¾-inch rectangles. Return to the oven for 5 more minutes, or until the whole surface of the sablé is golden brown; turn off the oven. Remove the sablé and transfer the rectangles to a rack to cool to room temperature; store them in an airtight container. Return the sablé breton trim to the warm oven until dried, about 30 minutes. Cool, and transfer the trim to a food processor. Pulse into fine crumbs; reserve for the croustillant tuile.
    For the Croustillant Tuile
    1. Preheat the oven to 350°F. Line a rimmed 18 × 13-inch baking sheet with a Silpat. Sift half of the powder over the baking sheet in an even layer. Bake for 3 minutes, or until the sugar is melted. Remove from the oven, cover with a sheet of parchment paper, and carefully flip the Silpat onto a flat surface. Peel off the Silpat, and with the aid of a ruler, cut the sugar into 4 triangles that are 3½ inches long and have a base of ¾ inch. Lift the triangles with an offset spatula and transfer to a flat tray. If the sugar becomes too brittle when cut or lifted, slide the parchment back onto the baking sheet and place in the oven for 30 seconds to soften. Cool the tuiles at room temperature and store in an airtight container.
    For the Baked Apple Confit
    1. Preheat the oven to 350°F. Line a baking sheet with parchment paper or a Silpat. Line an 8½ × 4½-inch loaf pan with nonstick cooking spray.
    2. Put half the sugar in a large, heavy-bottomed saucepan over medium heat. Melt until golden brown, stirring occasionally. Add the remaining sugar and continue to heat to a dark caramel, 340°F. Pour onto the prepared baking sheet and cool at room temperature until hardened, about 3 hours. With a blunt object, crack the hardened sugar into small pieces and transfer to a food processor. Pulse into a fine powder and shake through a fine-meshed sieve. Store in an airtight container; use as soon as possible to prevent clumping.
    3. Peel the apples and, using a Japanese Ciba Peel S turning slicer or a mandoline, cut into thin slices one at a time. Line the bottom of the prepared loaf pan with a single layer of apple slices, trimming the edges as needed, and use a fine-meshed sieve to dust the top with an even layer of caramel powder. Repeat the process until all of the apples have been layered.
    4. Cover the loaf pan with aluminum foil and bake for 1½ hours, or until the apples are dark caramel in color and tender when pierced with a cake tester. Remove from the oven and cool at room temperature. Freeze in the mold overnight and cut into four 3½ × ¾-inch rectangles; reserve the trim for the ice cream.
    For the Confit Honeycrisp Ice Cream
    1. In a heatproof bowl, whisk the yolks and sugar until smooth. In a medium saucepan, bring the milk and cream to a simmer. While whisking, gradually pour half of the hot cream into the egg yolk mixture. Gradually whisk the mixture back into the saucepan. Return the pan to medium heat and cook, while whisking, until it reaches 185°F. Remove from the heat and transfer the mixture to a blender with the reserved apple trim. Puree until smooth and strain through a fine-meshed sieve into a bowl set over ice; stir until well chilled. Spin in an ice cream machine according to the manufacturer’s instructions.
    For the Calvados Cream
    1. Up to 30 minutes before serving, in the bowl of an electric mixer fitted with a whisk, whip the mascarpone and powdered sugar until smooth. Stream in the cream while whisking on high speed to medium peaks. Add the calvados and transfer the cream to a piping bag fitted with a small tip; keep chilled.
    For the Green Apple Sauce
    1. Core and quarter the apples and juice them with a vegetable juicer. Combine the juice with the lemon juice and xanthan gum and blend with a hand blender. Chill until ready to serve.
    To Finish
    1. Slice the apple into very thin half-moons.
    2. For each serving, set a rectangle of apple confit on a sablé breton. Pipe the calvados cream on top in a zigzag pattern. Top with a croustillant tuile and transfer to a dessert plate, inside of a sugar ring set upright (if using). Garnish the plate with dots of green apple sauce topped with fresh sliced apple and a scoop of ice cream set on top of an apple slice to the side.