Whisk together the flour and fine salt in a medium bowl.

Beat the softened butter with confectioners' sugar until smooth and creamy, then add the vanilla extract.

Gradually add the flour mixture into the butter-sugar blend, mixing until the dough forms large clumps.

Carefully fold in the well-drained maraschino cherries and chocolate chips, distributing evenly.

Shape the dough into a 2-inch log, wrap tightly in plastic, and refrigerate 1 to 2 hours.

Preheat the oven to 325°F (163°C) and line a baking sheet with parchment paper.

Slice the chilled log into discs about 1/4 to 1/3 inch thick.

Arrange slices on the baking sheet, spaced an inch apart, and bake until the tops turn light golden.

Cool on the baking sheet 5 minutes, then transfer to a rack to cool completely.