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To make phyllo tartlet shells: Preheat oven to 325F (160C).
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Lightly coat 2 mini-muffin pans with nonstick cooking spray.
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In a small bowl, whisk together egg white, oil and salt.
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Lay a sheet of phyllo on a work surface and with a pastry brush, lightly coat it with the egg-white mixture.
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Lay a second sheet smoothly on top, taking care to line up the edges before setting the sheet down.
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(Once you set down the sheet, it cannot be moved.)
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Brush with the egg-white mixture and repeat with 1 more sheet.
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Lay a fourth sheet on top but do not brush it.
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With a knife, cut the dough into 4 strips lenghtwise and 5 strips crosswise, making 24 squares.
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Press squares into muffin cups and bake for 8 to 12 minutes, or until golden brown and crisp.
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Transfer the tartlets to a rack and let cool.
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Repeat the procedure with the remaining 4 sheets of phyllo and egg-white mixture.
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(The baked tartlet shells may be stored in a closed container at room temperature for 1 week or in the freezer for up to 2 months.)
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To make smoked trout filling: In a food processor, combine cream cheese and smoked trout; process until fairly smooth.
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Add scallions and horseradish and pulse until just combined.
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(Alternatively, finely mince the smoked trout with a knife and combine with the cream cheese, scallion and horseradish in a small bowl.)
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(The smoked filling may be made ahead and refrigerated for up to 2 days.)
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Shortly before serving, spoon or pipe about 1 heaping teaspoon of filling into each tartlet shell and garnish with shredded cucumber.