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1
Preheat the oven to 410u00b0F.
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2
Place the butter, vegetable oil, water, sugar, and salt in an oven-proof. Bake in the oven for 15-20 minutes, until the mixture is boiling and the edges turn golden brown.
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3
Carefully take the bowl out of the oven, and even more carefully, add the flour and mix until incorporated and it forms a soft dough. (The butter/water mixture will spit when you add the flour, so do not lean directly over it!)
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4
Let cool for about 15 minutes. Scoop the dough into a tart pan, and let cool for another 15 minutes or so.
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5
Meanwhile, make the apple compote. Peel and dice the apples, then place them in a medium pot with the water and sugar. Cook the apples over low heat for 45 minutes to 1 hour, until the apples have stewed down to a paste. Stir every 15 minutes or so and add some water if the mixture becomes too dry. Stir in the vanilla and let cool until just warm.
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6
Using your hands, shape the dough around the tart pan. Prick the bottom all over with a fork. Bake the tart at 410u00b0F for about 15 minutes, until the edges are slightly golden-brown.
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7
Lower the temperature of the oven to 350u00b0F. Spread the apple compote evenly over the crust.
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8
Thinly slice the apples for the topping. Toss the slices in lemon juice. Arrange them on top of the compote: start from the outer edge, overlapping the slices slightly, and work your way in. Bake the tart for about 20-25 minutes, or until the edges of the apple slices on top turn golden brown.
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9
Mix together the apricot jam and hot water, and brush over the top of the tart. Let cool until warm, then serve.
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10
Recipe and technique for the crust adapted from David Lebovitz. Recipe for the filling adapted from Tartelette.