STIR flour with cornstarch and salt in a medium bowl. Using a wooden spoon, stir butter with icing sugar and lemon zest in a large bowl until smooth. Stir in flour mixture, then cherries and nuts. (Dough will be slightly crumbly, but pliable.) Pour coarse sugar into a large, flat baking dish. Set aside.
DIVIDE dough into 2 portions. Place each on a piece of waxed paper. Form and roll into a log about 7 in. long and 1 1/2 in. wide. Roll each log in coarse sugar, pressing lightly so sugar adheres to dough. Roll log in waxed paper and twist ends. Chill until firm, about 1 hour or overnight.
PREHEAT oven to 350F. Line a baking sheet with parchment paper. Slice logs into 1/4-in.-thick cookies. Arrange on prepared sheet 2 in. apart. Cookies will spread as they bake. Bake in centre of oven until lightly golden, about 10 min. Remove from oven and let cookies cool on sheet for 1 min. Transfer to a rack and cool completely. Repeat with remaining dough. Store in an airtight container up to 1 week or keep dough refrigerated up to 1 month.