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1
Put oven racks in upper and lower thirds of oven and preheat oven to 400F.
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2
Line 2 large baking sheets with parchment paper.
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3
Heat butter in an 8-inch skillet over moderately low heat until foam subsides, then cook onion, stirring occasionally, until softened but not browned, about 2 minutes.
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4
Transfer to a bowl to cool.
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5
When onion is cool, add shrimp, Sherry, tarragon, salt, and pepper and stir until combined well.
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6
Roll out 1 sheet of pastry on a lightly floured surface into a 12-inch square.
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7
Cut into thirds in one direction, then into fourths in the other direction to make 12 (3- by 4-inch) rectangles.
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8
Cut each rectangle in half diagonally to form 2 triangles.
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9
Place 1 triangle on a work surface with longest edge nearest you, then put 1 teaspoon shrimp filling in center of triangle.
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10
Bring bottom corner of shortest side up to top point, then wrap remaining corner around resulting cone.
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11
Pinch to seal, then transfer to a lined baking sheet.
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12
Form more cornets in same manner, then repeat with remaining sheet of pastry.
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13
Chill first sheet of cornets, loosely covered, while making second.
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14
Whisk together egg and milk and lightly brush some of egg wash over top of pastries.
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15
Bake in upper and lower thirds of oven, switching position of sheets halfway through baking, until golden, 18 to 20 minutes total.
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16
Cool cornets on sheets on racks 5 minutes, then gently loosen from parchment with a spatula.
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17
Serve warm.
