For caramel sauce:
Bring sugar, cream, and butter to boil in heavy medium saucepan over medium-high heat, whisking constantly until sugar dissolves. Boil until caramel thickens enough to coat spoon thickly, whisking often, about 10 minutes. Sauce can be made a few days in advance. Warm it over low heat, whisking thoroughly to avoid burning.
Blend flour, powdered sugar, and salt in processor. Add butter and blend until coarse meal forms. Add egg yolks. Pulse until moist clumps form. Gather dough into ball; flatten into disk. Wrap and chill at least 1 hour. DO AHEAD Dough for tart crust can be made 1 day ahead. Keep chilled.
Whisk first 4 ingredients in large bowl to blend. Add apples and toss until evenly coated.
Preheat oven to 375°F. Roll out dough on lightly floured surface to 13-inch round. Transfer to 9-inch-diameter tart pan with removable bottom. Cut overhang even with top of pan sides. Press sides of dough to bring 1/4 inch above sides of pan. Arrange apple quarters, cut side down, in circle around outer edge of pan, fitting snugly. Cut remaining apple quarters lengthwise in half; stand in center of tart, fitting snugly.
Bake tart until apples are tender, about 1 hour 15 minutes. Remove tart from oven; brush with some of caramel sauce. Cool tart to room temperature. Rewarm remaining caramel sauce. Drizzle tart lightly with sauce. Serve, passing remaining sauce separately.
Bon Appétit, November 2006