In a food processor, combine granulated sugar, brown sugar and salt and process until no clumps of brown sugar remain, about 30 seconds Add the butter, egg yolk and both the extracts and process until smooth and creamy, about 20 seconds making sure to scrape down the bowl when needed. Add the flour and pulse until the mixture forms a dough, roughly 20 pulses. Trasfer the dough to a lightly floured counter and pat it into a 5-inch square. Wrap the dough tightly in plastic wrap and refrigerate for one hour.

In a small saucepan, heat the cherries and cherry jam or preserves over medium heat until just bubbly. Let the mixture cool completely, about 30 minutes. Process the jam in a dry, clean food processor until it's smooth, about 15-20 seconds.

Remove the dough from the fridge and roll it between two pieces of parchment paper into a 10-inch square, to about 1/4-inch thickness. Freeze until firm, about 15 minutes. Cut the dough into four 2 1/2-inch strips. Spread the cherry mixture evenly over three of the strips, then stack the strips with the jam side up, ending with the plain strip on top. Wrap the log tightly in plastic wrap and chill until firm, about 15-20 minutes.

Adjust your oven racks to the middle and lower levels and preheat until 350 degrees. Line two large baking sheets with parchment paper. Slice the chilled dough into 1/4-inch thick slices and place them 1 inch apart on your prepared sheets. Bake until the edges of the cookies are lightly golden, about 13-15 minutes, switching and rotating the trays halfway through baking time. Remove from oven and immediately transfer to wire racks. Repeat with any remaining dough. Let cookies cool before serving.