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1
To make the crust, in a medium bowl, combine the flour, sugar and salt.
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2
Add the butter and cut in with a pastry blender or 2 forks until the mixture resembles small pebbles.
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3
Stir in just enough of the ice water so the dough forms a rough ball.
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4
Place the dough onto a lightly floured surface and push the dough with the heels of your hands into a 6-by-4-inch rectangle.
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5
Fold up the bottom 1/3 of the rectangle, then fold the top 1/3 down, as if folding a letter.
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6
Turn dough 90 degrees and repeat, rolling out the dough to a 6-by-4-inch rectangle and refolding.
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7
Cover with plastic wrap and chill for 1 hour.
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8
Remove the dough from the refrigerator and set aside for 10 minutes to soften slightly, so it is easy to handle.
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9
Roll out the dough into a 13-inch circle.
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10
Fit the dough into a 10- 1/2-inch tart pan with a removable bottom.
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11
Press the dough gently into place, prick the bottom with a fork and cover with plastic wrap.
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12
Chill for 1 hour.
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13
Preheat the oven to 425 degrees.
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14
To make the filling and glaze, take the pastry from the refrigerator.
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15
Core, peel and halve the apples.
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16
With the flat side of the apple down, cut crosswise into thin slices.
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17
Fan them concentrically, reserving about 6 slices for the center of the tart.
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18
Sprinkle the apples with sugar and dot with butter.
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19
Bake until the crust is brown and the apples lightly caramelized, about 1 hour.
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20
Remove the tart from the oven and carefully remove the sides of the pan.
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21
Slide the tart onto a rack to cool to room temperature.
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22
In a nonreactive saucepan, melt the apricot preserves with the rum until the mixture is smooth, about 5 minutes.
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23
Strain the glaze through a fine mesh sieve and brush over the tart.
