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1
Preheat the oven to 375 degrees F.
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2
Mix the flour, butter, sugar, and salt quickly with your fingertips until the butter is in pieces about the size of dried beans.
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3
Quickly stir the water into the mixture and then gather up the dough onto a sheet of plastic wrap and press it into a flat dish shape.
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4
Refrigerate dough for 1 hour.
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5
Line a cookie sheet or jelly roll pan with parchment or a silicon pad.
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6
Roll the dough out onto a lightly floured surface into a rectangle about 15-inches long by 10-inches wide, with rough edges.
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7
Roll the dough up onto your rolling pin and then unroll it directly onto the lined pan.
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8
Roast the hazelnuts on a cookie sheet for 7 or 8 minutes.
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9
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.
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10
Spread the frangipane on the dough, stopping about 1 1/2-inches from the outer edge on all sides.
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11
Peel the apples, remove the cores, and cut them into 1/2-inch thick slices.
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12
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.
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13
Fold the edge of the dough back over the apples to make a 1 to 1 1/2-inch border of dough.
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14
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.
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15
Break the remaining 2 tablespoons butter into pieces and scatter them over the tart.
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16
Bake for 1 hour.
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17
The dough should be nicely crystallized all over.
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18
Remove the finished tart from the oven and cool on a rack until lukewarm.
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19
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.
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20
Serve at room temperature cut into little wedges, with plain cream, sour cream, creme fraiche, or ice cream, if desired.
