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For Pastry Dough:.
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Blend together flour, butter, shortening, and salt in a bowl with your fingertips or a pastry blender (or pulse in a food processor) just until mixture resembles coarse meal with some small (roughly pea-size) butter lumps.
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5 tablespoons for a double-crust pie evenly over mixture and gently stir with a fork (or pulse) until incorporated.
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Squeeze a small handful of dough: If it doesn't hold together, add more ice water 1/2 tablespoon at a time, stirring (or pulsing) until incorporated.
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Do not overwork dough, or pastry will be tough.
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Turn out dough onto a work surface.
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For a single-crust pie, divide dough into 4 portions; for a double-crust pie, divide dough into 8 portions.
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With heel of your hand, smear each portion once or twice in a forward motion to help distribute fat.
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Gather all dough together with pastry scraper.
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For a single-crust pie, press into a ball, then flatten into a 5-inch disk.
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For a double-crust pie, divide dough into 2 pieces, with one slightly larger, then form each into a ball and flatten each into a 5-inch disk.
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If dough is sticky, dust lightly with additional flour.
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Wrap each disk in plastic wrap and chill until firm, at least 1 hour.
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Make lime curd: Whisk together eggs, sugar, and lime juice in a 2-quart heavy saucepan until combined.
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Add butter and cook over moderately low heat, whisking constantly, until curd is thick enough to hold marks of the whisk and first bubbles appear on surface, 8 to 10 minutes.
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Immediately pour through a fine-mesh sieve into a bowl, discarding solids.
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Cool to room temperature, stirring occasionally.
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Stir in zest, then chill, covered, at least 1 hour.
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Make pastry rounds: Put oven rack in middle position and preheat oven to 350F Line 1 baking sheet with parchment paper.
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Roll out dough into a 15-inch round (pastry will be thin) on a lightly floured surface with a lightly floured rolling pin.
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Cut out 18 rounds with cookie cutter and arrange 1/2 inch apart on lined baking sheet.
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Prick each round several times with a fork, then cover rounds with another sheet of parchment and weight with second baking sheet.
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Bake until rounds are pale golden, 15 to 20 minutes.
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Remove top baking sheet and parchment and transfer rounds to racks to cool.
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Sprinkle each round evenly with 1/2 teaspoon superfine sugar and carefully caramelize with a blowtorch (sugar burns easily).
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Make glazed fruit and assemble desserts: Boil confectioners sugar, water, and lime juice in a 12-inch heavy skillet over moderate heat, stirring occasionally, until slightly thickened, about 2 minutes.
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Remove from heat and add berries, gently tossing to coat.
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(There will be just enough to glaze berries; they will give off a small amount of juice as they cool.
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).
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Cool berries 5 minutes.
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Put 1 tablespoon of curd on each of 6 plates.
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Stack 3 rounds on each plate, layering rounds with some of curd and glazed berries, then drizzle plates with some syrup.
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Cooks' notes:.
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Lime curd can be chilled up to 3 days ahead.
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Pastry rounds can be baked and caramelized 1 day ahead, then cooled and kept in an airtight container at room temperature.
