Make the dough:

In a large bowl blend the flour, the butter, the shortening, the sugar, and the salt until the mixture resembles meal. Add 3 tablespoons of the ice water, toss the mixture until the water is incorporated, adding as much of the remaining water as is necessary to form a dough, and form the dough into a ball. Dust the dough with flour and chill it, wrapped in wax paper, for 1 hour.

Preheat the oven to 425F.

On a lightly floured surface roll out the dough into a round slightly larger than the pie plate and drape it over the filling. Tuck the dough down inside the edge of the pie plate and prick it in 4 places. Bake the tart in the middle of the oven for 20 minutes, or until the juices are bubbling and the crust is golden. If any apples stick to the pie plate rearrange them on the tart carefully. Serve the tart warm or at room temperature with the creme fraiche.

Make the filling:

In a large heavy skillet melt the butter over moderately high heat, stir in the sugar, the Calvados or applejack, the zest, and the cinnamon sticks, and boil the mixture for 1 minute. Stir in the apples, peeled, cored, and quartered, and cook the mixture, stirring frequently, for 30 minutes, or until the apples are glazed and the syrup is beginning to thicken. Discard the zest and the cinnamon sticks, add the lemon juice, and cook the mixture over high heat for 10 minutes, or until the syrup is almost completely evaporated and the apples are tender and a rich golden brown. Spoon the filling into an 11- by 2-inch (1 1/2-quart capacity) glass pie plate, tamping the apples down with a metal spatula.