For cookies, in bowl of your stand mixer fitted with paddle attachment mix butter and granulated sugar together for 1 minute on medium speed until combined. Add in vanilla extract and cherry juice and mix until smooth.
Turn mixer to low and add in flour until incorporated, scraping sides and bottom of bowl as necessary. Dough will be thick. Fold in chopped cherries.
Cover dough and refrigerate for at least 1 hour.
Preheat oven to 375°F. Line baking sheets with parchment paper and set aside.
Scoop out chilled dough using a small (1- tablespoon) cookie scoop. Roll the dough into balls and place on the prepared baking sheet 2- inches apart.
Bake for 12 - 15 minutes until set and edges just begin to turn golden.
Transfer cookies to a wire rack to cool completely.
For glaze, in a medium bowl whisk together powdered sugar, lime juice, and zest.
Dip tops of cooled cookies into glaze, or alternately you can spoon glaze on top of cookies.