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1
Reserve a quarter of dough for another use.
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2
On a floured surface with a floured rolling pin roll out remaining dough into a 14-inch round (about 1/8 inch thick) and fit into an 11- by 1 1/4-inch round tart pan with a removable fluted rim.
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3
Trim dough flush with rim.
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4
(Don't worry if dough cracks; press dough together to patch any holes.)
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5
Prick shell lightly all over with a fork.
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6
Chill shell, covered, 30 minutes.
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7
Preheat oven to 425F.
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8
Line shell with foil and fill with pie weights or raw rice.
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9
Bake shell in middle of oven 15 minutes and remove weights or rice.
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10
Bake shell until pale golden, about 10 minutes more, and transfer to a rack to cool.
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11
Reduce temperature to 350F.
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12
Chop hazelnuts.
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13
Peel kiwifruits and quarter lengthwise.
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14
Halve vanilla bean half lengthwise and scrape seeds into a small saucepan, reserving pod for another use.
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15
Add butter and melt over moderately low heat until golden brown.
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16
Cool mixture to room temperature.
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17
Into a small bowl sift flour.
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18
In a bowl with an electric mixer beat eggs with sugar and rum until thick and pale.
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19
Fold in flour gently but thoroughly.
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20
Fold butter into egg mixture gently but thoroughly.
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21
Arrange kiwifruits evenly in one layer in tart shell and pour filling over them, spreading evenly.
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22
Sprinkle hazelnuts over filling and bake in middle of oven 35 minutes, or until top is golden.
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23
Cool tart in pan on a rack.
