1. Soak chopped dried cherries in cherry liqueur 1 hour.
2. Beat butter at medium speed with an electric mixer until creamy. Gradually add sugar, beating until smooth. Stir in cocoa, vanilla, and soaked cherries until blended.
3. Stir together flour and next 2 ingredients. Gradually add flour mixture to butter mixture, beating at low speed until blended.
4. Preheat oven to 350°. Shape dough into 1-inch balls (about 1 Tbsp. per ball), and place 2 inches apart on parchment paper-lined baking sheets. Press thumb or end of a wooden spoon into each ball, forming an indentation.
5. Bake at 350° for 12 to 14 minutes or until edges are golden. Cool on baking sheets 1 minute; transfer to wire racks. Cool completely.
6. Microwave white chocolate morsels and cream in a microwave-safe bowl at HIGH 1 minute or until melted and smooth, stirring at 30-second intervals. Spoon 1/2 tsp. chocolate mixture into each indentation. Let stand until white chocolate mixture is firm (about 1 hour). Store in airtight containers.