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1
Make filling: Process cherries, jam, and sugar in a food processor until coarsely pureed. Transfer to a small saucepan. Bring to a boil over medium heat, stirring occasionally. Remove from heat, and stir in almond extract. Let cool completely.
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2
Make dough: Whisk together flour, cornmeal, baking powder, and salt in a bowl. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy, 2 to 4 minutes. Mix in egg and vanilla. Reduce speed to low. Add flour mixture; mix until just combined.
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3
Transfer dough to a work surface. Divide into four equal pieces. Roll one piece of dough between two sheets of parchment paper to a 3 1/2-by-9-inch rectangle about 1/4 inch thick. Repeat with the remaining dough pieces. Transfer with parchment to a baking sheet, and freeze 30 minutes.
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4
Assemble cookies: Remove top pieces of parchment. Spread 1/3 of the filling evenly over one rectangle. Top with another rectangle; remove parchment. Repeat with remaining filling and rectangles, leaving the top triangle uncoated. Wrap in plastic, and freeze 1 hour.
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5
Preheat oven to 350 degrees. Trim dough to 3 1/4-by-8 1/2-inch brick. Cut into 1/4-inch-thick slices. Space 2 1/2 inches apart on baking sheets lined with nonstick baking mats (such as Slipats). Bake cookies, rotating sheets halfway through, until edges are pale golden brown, 12 to 15 minutes. Let cool on sheets on wire racks.
