In large bowl, combine brown sugar, cornstarch, flour and salt; stir well.
Add butter and mix with electric mixer on low speed until the mixture is coarse and crumbly.
Add cherries and vanilla and mix until the cherries are evenly distributed, 20 to 30 seconds.
Scrape half of dough from bowl onto a sheet of parchment paper and roll the dough out ¼ inch thick. Lift parchment paper onto a rimmed baking sheet and cover with plastic wrap. Repeat with remaining piece of dough.
Chill both baking sheets in the refrigerator for at least 1 hour.
Preheat oven to 325°F Remove baking sheets from the refrigerator. Using a sharp knife or cookie cutter, cut the dough into 2-inch rounds (or shape of your choice).
Place cookies on baking sheets. Keep cookies refrigerated until ready to bake.
Bake cookies, one sheet at a time, on center rack of oven for 20 to 25 minutes each.
Cool on the baking sheet for at least 20 minutes, then dust with confectioners’ sugar.