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lightly floured surface into a rectangle about 15-inches long by 10-inches wide, with rough edges. Roll the dough up onto your rolling pin and then unroll it directly onto the lined pan.
Roast the hazelnuts on a cookie sheet for 7 or 8 minutes. Transfer the nuts to a food processor, add the 1/4 cup sugar, egg, 1 tablespoon butter, and vanilla, and process until a creamy paste forms. Spread the frangipane on the dough, stopping about 1 1/2-inches from the outer edge on all sides.
Peel the apples, remove the cores, and cut them into 1/2-inch thick slices. Arrange them attractively in a slightly overlapping pattern, like the tiles of a roof, on the pastry dough so that the apples cover the frangipane. Fold the edge of the dough back over the apples to make a 1 to 1 1/2-inch border of dough. Increase the oven temperature to 400 degrees F. Sprinkle 2 tablespoons sugar over the apples, letting a little of the sugar fall onto the border to help crystallize the dough. Break the remaining 2 tablespoons butter into pieces and scatter them over the tart. Bake for 1 hour. The dough should be nicely crystallized all over.
Remove the finished tart from the oven and cool on a rack until lukewarm. Dilute the apricot preserves with the calvados or water and glaze the surface of the tart, spreading it carefully on the apples with the underside of a spoon. Serve at room temperature cut into little wedges, with
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