In a food processor fitted with a metal blade, process the dates, almonds, and cherries until they are coarse crumbs that will stick together easily.
Place the mixture onto a sheet pan lined with parchment.
Cover the mixture with plastic wrap and roll it out. Fold the edges of the paper over and firm up the edges. Continue to do this, squaring off the edges and thickening them up.
Cut into squares. Chill in an airtight container until ready to serve.
For longer storage, freeze the bars until ready to serve.