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1
In a bowl, stir the 1 1/3 cups flour with the sugar and salt.
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2
Using your fingers, rub the butter and shortening into the flour until the mixture resembles coarse crumbs.
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3
Sprinkle the ice water on top and stir just until combined.
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4
If the dough is sticky, work in 1 more tablespoon of flour.
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5
Shape the dough into a ball and pat it out to a 6-inch disk.
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6
Wrap in wax paper and refrigerate for at least 1 hour or overnight.
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7
Preheat the oven to 400.
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8
On a lightly floured surface, roll out the dough to a 13-inch circle.
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9
Transfer the dough to an 11-by-1-inch tart pan with a removable bottom.
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10
Trim the overhang flush with the rim and prick the bottom all over with a fork.
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11
Butter a large piece of foil, set it buttered side down on the dough and fill with rice or pie weights.
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12
Bake for about 20 minutes, or until the edges are golden.
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13
Remove the foil and weights and bake for about 5 minutes longer until the bottom is just cooked through.
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14
Let cool slightly.
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15
Lower the oven temperature to 375.
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16
In a food processor, pulse the walnuts until finely ground but not pasty.
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17
In a medium bowl, beat the butter with 1/3 cup of the sugar.
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18
Beat in the egg, rum and flour until blended.
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19
Fold in the walnuts; the mixture may look curdled, but it won't affect the tart.
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20
Peel, halve and core the apples and cut them lengthwise into 1/8-inch slices.
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21
Transfer to a medium bowl and toss with the lemon juice, cinnamon and nutmeg.
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22
Spread the walnut mixture evenly in the tart shell.
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23
Arrange the apple slices on top in concentric circles and sprinkle with the remaining 2 tablespoons sugar.
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24
Bake the tart for about 35 minutes, or until the apples are browned at the edges and tender when pierced with a knife.
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25
Let cool slightly on a rack.
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26
In a small saucepan, melt the apple jelly over low heat, stirring, until smooth.
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27
(If using apricot jam, strain it after melting.)
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28
Brush the apples with the jelly.
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29
(The tart can be kept at room temperature for up to 4 hours.
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30
It can be rewarmed gently in a 325 oven.)
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31
Remove the sides of the pan and serve the tart warm.