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1
Drain yogurt in a cheesecloth-lined sieve or colander set over a bowl, covered and chilled, 8 hours.
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2
Preheat oven to 350F.
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3
Put stack of phyllo on a work surface and cover stack with 2 overlapping sheets of plastic wrap and then a damp kitchen towel.
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4
Stir together butter and oil.
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5
Arrange 1 phyllo sheet on a large parchment-lined baking sheet, then spread with one fourth of butter mixture using a dampened pastry brush.
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6
Sprinkle with 1 teaspoon granulated sugar.
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7
Top with 3 more layers in same manner as first with remaining phyllo and butter mixture and 3 teaspoons granulated sugar.
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8
Cut stack into 12 rectangles (2 lengthwise cuts, 3 crosswise) and bake in middle of oven until crisp and golden brown, about 10 minutes.
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9
Cool in pan on a rack.
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10
Scrape seeds from vanilla bean into a bowl using a small sharp knife.
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11
Stir in drained yogurt, sour cream, and 1 tablespoon brown sugar.
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12
Heat a large nonstick skillet over moderately high heat.
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13
Add apricots and sprinkle with remaining 2 teaspoons granulated sugar.
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14
Gently toss until apricots are warm and tender, 2 to 3 minutes.
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15
Transfer apricots to a bowl with a slotted spoon.
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16
Add water and remaining teaspoon brown sugar to skillet and deglaze by boiling over moderately high heat, scraping up brown bits, until reduced by about half.
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17
Toss apricots in warm syrup.
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18
Place 1 phyllo rectangle on a plate and top with 3 apricot pieces and 1 generous tablespoon yogurt mixture.
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19
Make 2 more layers with phyllo squares, apricots, and yogurt mixture.
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20
Make 3 more napoleons in same manner.
