Tarte Tatin Peel the apples, cut in quarters, remove the cores (cutting each quarter at the core so it has a flat side), and toss the quarters in a large bowl with the lemon juice and 1/2 cup of the sugar. Let rest for 1/2 hour.
Melt 4 tablespoons of the butter in a round, 10" cast-iron skillet over medium-high heat. Cover with the remaining cup of sugar, sprinkled over the butter in an even layer. Add the apple quarters to the pan, arranging them in a decorative pattern, rounded side down. Top the apples with the remaining 2 tablespoons of butter, cut into little bits.
Cook the apples over medium heat for approximately 40 minutes, occasionally spooning the bubbling liquid over the apples. This part of the recipe takes almost constant surveillance. In a few minutes, you will begin to see brown caramel bubbling up in the part of the pan over direct heat. Immediately shift the pan so that other non-browned parts go over the direct heat. Over 40 minutes, you may have to shift the pan a dozen times or more to get things evenly browned. The apples are ready when the liquid in the pan has turned to a thick dark-tan ooze. The apples should still be slightly resilient. Do not allow the apples to get entirely soft, or the liquid to turn dark brown. This part of the tarte tatin can be prepared hours in advance, or you can proceed immediately with the recipe.
Pre-heat an oven to 375 degrees.
Flour a work surface and place the sheet of puff pastry on it. Roll out the pastry until it is slightly larger than the interior of the apple pan. Lay it over the apples, tucking any protruding edges under the apples in the pan. Place the apple pan in the oven and cook for approximately 30 minutes, or until the puff pastry has risen and cooked. The pastry should be dry and flaky inside. Remove from the oven, and let the tarte rest for a few minutes. Place a large, round platter over the tarte and flip it over, releasing the tarte from the pan. The browned apples will be on top, the pastry on the bottom. Serve hot, if desired. You can also serve this tarte warm--my preference--about one hour after cooking. You can also serve it room temperature, or cold. Serve with Vanilla Creme Fraiche, if desired.
Vanilla Creme Fraiche
Blend ingredients together in a mixing bowl. Pour along tarte tatin.