Divide the pastry into 2 parts, one a little larger than the other. Wrap the larger piece in plastic wrap and reserve. On a lightly floured surface, roll the smaller piece into a round, 1/8 to 1/4-inch thick, large enough to overlap a 10 by 2-inch pie plate. Arrange in the pie plate and even with a sharp knife, leaving about a 1/2-inch overhang. (Add the trimmings to the reserved dough). Tuck the overhang back under, making a slightly thicker edging. Chill for 30 minutes. If using a glass pie plate, remove from the refrigerator 15 minutes before filling.
On a lightly floured surface, roll out the reserved piece of dough into a 12-inch square, about 1/4-inch thick. Cut out a piece of cardboard, 1/2-inch wide and 10 or 12 inches long. Wrap the strip in plastic wrap and use as a guide. With a sharp knife or a pastry cutter, cut the dough into 20 (1/2-inch) strips. Lay 10 strips vertically on the back of a large baking pan, leaving a very small space between strips. Weave a lattice pattern by placing each of the remaining strips over and under horizontally. (It's easier to weave if the dough is not too firm, but it can't be too soft, either. If it's too soft, refrigerate for a little while and then continue). To weave, turn back every other strip of dough (1, 3, 5, etc.), lay a horizontal strip across, as close to the top as possible, and return the turned-back strips to the original length.
For the next row, alternate the strips that you turn back (2, 4, 6, etc.) and again place a horizontal strip across, close to the first strip. Repeat this procedure until all the strips are used. Refrigerate just until firm. Using a 9-inch cardboard round, a plate, or a pot cover as a guide, cut out a 9-inch circle of latticework and refrigerate on the baking pan until needed. (Excess dough can be wrapped and refrigerated or frozen for future use).
Peel, core and quarter the apples. Cut into 1/4-inch slices. In 2 or 3 large skillets, melt the butter (2 or 3 tablespoons in each skillet, depending upon how many you use) and brown. The butter will have a slightly nutty aroma. Divide the apples, arrange in the pans, and coat with the butter. Sprinkle in the sugar and over medium-high heat, saute the apples until lightly caramelized and tender, 15 to 20 minutes, turning often so that the apples cook evenly. Pour in 1 tablespoon of Calvados and the brandy and cook until the alcohol burns off. Pour in the cream and stir through. Transfer and spread over a large baking tray to cool.
Preheat the oven to 400 degrees F.
Warm the remaining 1/4 cup Calvados. Combine the chopped prunes, apricots, and figs in a small bowl. Pour the Calvados over and let plump.
In a large bowl, combine the cooled apples and the plumped dried fruit. Stir in the lemon juice, cinnamon, lemon and orange zests, and nutmeg, and mix well. Spoon the filling into the prepared pie plate. Using a wide spatula, carefully transfer the 9-inch latticework circle and arrange on top of the filling. Brush the latticework with egg white and sprinkle with the crystallized sugar. Bake 30 minutes, turn the oven down to 350 degrees F and bake 35 to 40 minutes longer, until the crust is golden brown. Cool on a rack. Serve warm.
In a food processor fitted with the steel blade, combine the flour and sugar. Add the butter and process until the texture resembles fine meal.
In a small bowl, whisk together the yolks and 1 tablespoon of the cream. Scrape into the machine and process until a ball begins to form, using the additional tablespoon of cream, if necessary. Remove the dough from the machine, and on a lightly floured surface, press down into a circle. Wrap in plastic wrap and refrigerate for at least 1 hour.