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1
Position racks in the middle and lower third of the oven; preheat to 350 degrees F. Make the dough: Pulse the flour, granulated sugar and salt in a food processor until combined.
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2
Add the butter; pulse until the mixture looks like coarse meal with pea-size bits of butter.
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3
Beat the egg with 1 tablespoon ice water in a bowl, then add to the processor and pulse once or twice.
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4
(Stop before the dough gathers into a ball.)
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5
Turn out onto a sheet of plastic wrap and pat into a disk.
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6
Wrap tightly and refrigerate until firm, at least 1 hour.
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7
Meanwhile, prepare the filling: Toast the walnuts on a baking sheet on the middle oven rack until golden, 7 to 8 minutes; let cool.
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8
Process the nuts, 1/4 cup granulated sugar, the egg, 1 tablespoon butter, the vanilla and salt in a clean food processor to make a creamy paste.
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9
Line a flat baking sheet (or an upside-down rimmed one) with parchment paper.
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10
Roll the dough into a 12-inch round on a floured surface.
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11
Roll the dough up onto the rolling pin, then unroll onto the parchment.
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12
Spread the walnut filling over the dough, leaving a 1 1/2-inch border around the edges.
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13
Chill while you prepare the apples.
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14
Increase the oven temperature to 400 degrees F. Peel, core and halve the apples, then cut each half into 8 wedges.
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15
Arrange over the filling in a circular pattern, slightly overlapping.
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16
Fold the edges of the dough inward, pleating it.
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17
Sprinkle the apples with the remaining 1 tablespoon granulated sugar and 2 tablespoons butter.
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18
Bake the galette on the middle oven rack until golden, 40 to 45 minutes.
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19
(Put a baking sheet on the lower rack to catch any drips.)
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20
Cool on a rack.
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21
Whisk 1 tablespoon water and the preserves in a bowl.
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22
Strain, then brush over the apples.
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23
Dust with confectioners' sugar, if desired.
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24
Photographs by Con Poulos
