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For the pate brisee:
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In the bowl of an electric mixer, use dough hook on low speed to combine the flour, salt, and sugar.
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Add the butter by chunks.
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When the mixture is the consistency of coarse meal, add the water and mix thoroughly, but do not overmixed.
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The dough will be moist (but it will be tough if overmixed).
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Gently shape the dough into a ball, wrap in plastic wrap, and refrigerate at least 4 hours or overnight
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When ready to hake, divide the dough into 6 equal pieces.
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On a lightly floured board, roll each piece 1/8 inch thick and press into a 4-to 4 1/2-inch tart pan, making sure it extends 3/4 inch up the sides of the pan.
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Refrigerate 1 to 2 hours.
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Preheat the oven to 400F.
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Line each shell with aluminum foil and fill with beans or pie weights.
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Bake 15 minutes, then remove the foil and beans, reduce the temperature to 375F., and bake until light golden brown, about 10 minutes.
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For the onion confit:
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In a large skillet, heat the oil and butter over high heat until shimmering.
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Add tbe onions, sprinkle with the sugar, and cook without stirring for 5 minutes.
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Stir, then continue to cook, stirring occasionally, for another 5 minutes.
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Reduce the heat to medium-high and cook 5 minutes more.
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Raise the heat to high, add 1/2 cup of stock, and boil for 1 minute.
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Add the vinegar and continue cooking 10 to 12 minutes, reducing the heat to medium-high as the onions begin to brown.
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Taste and add stock if the onions are too tart, or vinegar if they are too sweet.
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Season with salt and pepper and keep warm.
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To serve:
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Remove the shells from the tart pans.
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Spoon about 1/2 cup of the onions into each shell, sprinkle with the minced chives, and place on individual serving plates.
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Drizzle each plate with the optional chive oil.
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Variation:
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Substitute balsamic vinegar for sherry vinegar, Perfect Flaky Piecrust or frozen purchased puff pastry for the pate brisee.