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1
In a saucepan, combine 3/4 cup of the milk with the sugar and basil; bring to a simmer.
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2
Remove the milk from the heat and let stand for 15 minutes.
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3
Remove the basil and squeeze any milk back into the pan; discard the basil.
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4
In a small bowl, whisk the remaining 1/4 cup of milk with the yolks and cornstarch until smooth.
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5
Slowly whisk the egg yolk mixture into the warm milk; bring to a simmer over moderate heat, whisking constantly until very thick, 2 minutes.
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6
Remove from the heat and whisk in the butter until melted.
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7
Scrape the cream into a bowl.
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8
Press a piece of plastic wrap directly on the surface and refrigerate until chilled, 2 hours.
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9
Preheat the oven to 375.
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10
Spray a 14-by-4 1/2-inch rectangular tart pan with a removable bottom with nonstick cooking spray.
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11
In the bowl of a standing mixer, beat the hard-boiled egg yolk with the butter and sugar at medium speed until smooth, about 2 minutes.
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12
Add the flour, potato starch and salt and beat at low speed until just combined.
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13
Using lightly floured hands, press the dough evenly over the bottom and up the side of the tart pan.
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14
Refrigerate the crust for 30 minutes, or until chilled.
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15
Bake the crust for about 25 minutes, until golden.
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16
Transfer the crust to a rack and let stand until cooled, about 1 hour.
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17
Increase the oven temperature to 450.
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18
Line a baking sheet with parchment paper.
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19
Arrange the apricot halves cut side up on the paper and sprinkle all over with the sugar.
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20
Roast for about 20 minutes, until the apricots are tender and lightly browned.
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21
Let the apricots stand until completely cooled, about 30 minutes.
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22
Unmold the crust and transfer it to a serving plate.
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23
Using a small offset spatula, spread the cream evenly in the crust.
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24
Arrange the apricots on the cream, cut sides down, and brush with the melted jam.
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25
Cut the tart crosswise into strips and serve at once.
