Thaw puff pastry dough according to the package directions. Do not allow it to get too warm or it will be difficult to work with.
Place one puff pastry sheet on a lightly floured work surface. Roll dough to 0.125-inch thickness (1/8th-inch). Cut out three, 6 to 7-inch round circles with a sharp knife. I used a small bowl as a template.
Stack the dough circles on a plate separated by parchment paper. Repeat the process with the second sheet of dough. Cover and chill in the refrigerator for 30 minutes.
Remove pits/kernels from the cherries with a cherry pitter. Place in a mixing bowl with lemon zest and juice, sugar, and starch. Mix together to thoroughly coat. Set aside on the counter.
Place the dough circles on the baking sheet one at a time, filling each with 0.33 cup of cherry mixture. (Stir filling before using). Fold over the dough and pleat the dough edges gently up around the filling mixture on all six tarts. Place the baking sheet in the refrigerator and chill for 10 minutes.
Preheat over to 425 degrees. Line a baking sheet with parchment paper or silicone liner. Set aside.
Beat egg in a small bowl with a fork. Brush on the edges of the tarts and sprinkle with sugar, if using.
Place into the oven and bake until the pastry is golden brown, 15 to 20 minutes depending on your oven. Cool on a wire rack.
Serve warm or at room temperature sprinkled with lemon zest or with ice cream or whipped cream.
Notes
Can I use frozen cherries?
Yes you can, and you do not need to thaw them ahead of time. Just mix them with the other filling ingredients.
How do you store leftover tarts?
Place in an airtight container if using within two days. For longer storage, cover tightly with plastic wrap and freeze for up to one month. To thaw, place in the refrigerator for 24 hours.
Can I use sour cherries?
Yes! Just omit the lemon juice to avoid your tarts being too sour/tart. If the cherries are very sour, add a tablespoon or two extra sugar to the mixture.