Preheat the oven to 325°F and line a baking sheet with parchment paper.
In a large bowl, cream together the butter and powdered sugar until light and fluffy.
Mix in the vanilla extract.
Gradually add the flour, mixing until well combined.
Fold in the chopped maraschino cherries and white chocolate.
Shape the dough into 1.5-inch balls and place them on the prepared baking sheet, spacing them about 2 inches apart.
Flatten each ball slightly with your hands.
Bake for 12-15 minutes, or until the cookies are set but not browned.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.