Mix powdered sugar, sweetened condensed milk, softened butter, and vanilla in a large bowl with your hands until smooth.
Cover and chill about an hour.
Roll into 1" balls and place a well drained and dried off cherry in the center. Place on a sheet pan covered with wax paper or parchment paper. Work quickly here!
If the filling mixture gets too warm, it will become too sticky to work with. Just place back into the refrigerator for 30 minutes to an hour to re-chill.
Freeze balls for at least 2 hours - overnight is even better.
Place the chocolate chips in a microwave-safe bowl. Microwave on High in 30 second increments, stirring between each increment, until melted and smooth.
Dip frozen balls into melted chocolate. Cool on wax paper.
Store in the refrigerator, tightly covered, for 1 week. Freeze for up to 1 month.