To make the cherry filing, use a blender, immersion blender or food processor to puree the cherries, jam and sugar. Cook in small saucepan over medium heat until it comes to a boil. Remove from heat. Stir in vanilla extract. Let cool.
To make dough, in a large bowl cream butter and sugar until light and fluffy. Add egg and vanilla and mix to combine.In another bowl, whisk together flour, cornmeal, baking powder, salt and orange zest. Add to butter mixture then mix gently until just combined.
Divide dough into four equal portions. Place one portion between two pieces of parchment paper or waxed paper and roll out intoa 3 ½ x 9-inch rectangle. Repeat with remaining three dough portions. Stack each sheet, with paper separators, on a baking sheet and place in freezer for 30 minutes.
To assemble cookies, remove dough from freezer and carefully peel back top piece of paper. Spread 1/3 of cherry mixture over first sheet of dough. Place another sheet over the cherry layer, spread with 1/3 of cherry mixture. Repeat once more, then place fourth sheet on top (without covering with jam.)
Trim shaggy edges with a sharp knife so you have a clean rectangle Cut and press scraps together to make a second, smaller rectangle. Wrap both tightly with plastic wrap and freeze for at least an hour or up to a month.
When ready to bake, preheat oven to 350º F. Line baking sheets with parchment paper. Slice frozen dough into 1/4-inch thick rectangles and place on baking sheets about 2-3 inches apart. Bake at 350º F until light golden brown at edges, about 10 to 13 minutes. Transfer to a wire rack to cool. Store in an airtight container for up to two weeks.