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Special equipment: a 10-by-15-inch rimmed baking sheet
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For the filling: Put the cherries, granulated sugar, chocolate, cornstarch, lemon juice, vanilla and almond extracts and salt in a large bowl.
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Toss until the cornstarch dissolves.
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Let stand at room temperature until juicy, about 30 minutes.
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(If using frozen cherries, leave them frozen and toss them with the above ingredients).
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Adjust an oven rack to the lower third of the oven and preheat the oven to 375 degrees F. Grease the bottom and sides of a 10-by-15-inch baking sheet with butter.
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For the crust: To form the bottom crust, place 1 pie crust between two large pieces of floured parchment paper and roll into a 14-inch round.
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Lay the round over half of the prepared baking sheet; there will be overhang on the edges.
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Repeat the rolling process with a second pie crust.
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Lay it over the remaining exposed side of the baking sheet so that the two crusts overlap in the center of the pan; there will be overhang on the edges.
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Press together the overlapping crusts to make a tight seal.
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Transfer the filling to the crust and spread in an even layer.
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Dot the top with the butter.
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For the lattice crust: Repeat rolling the remaining 2 pie crusts into two 14-inch rounds.
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With a chef's knife or a pizza cutter, cut each crust into 1-inch-wide strips.
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Lay half the strips diagonally across the entire pie, about 1-inch apart.
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Weave the remaining strips diagonally across the first strips to make a lattice pattern.
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Trim the the lattice ends leaving an overhang, Press together the ends and the bottom edge of the crust to seal, then fold and crimp the edge as desired.
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Brush the lattice and edge of the crust with the cream and sprinkle generously with some granulated sugar.
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Bake until the crust is golden brown and the filling is bubbly, 45 to 55 minutes.
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(If the crust browns too quickly during baking, cover the pie loosely with foil.)
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Let cool.
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For the topping: Meanwhile, whip the cream, sour cream and brown sugar in a large bowl to medium peaks.
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Cover and refrigerate until ready to use.
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Serve the pie warm or at room temperature with dollops of the whipped topping.