Place a sheet of parchment on a rimmed baking sheet and set aside.
Melt chocolate in the top of double boiler with simmering water beneath. Heat gently, stirring until fully melted. Remove from heat and allow to cool slightly.
In the bowl of electric mixer, beat butter, sifted confectioners sugar and cocoa until light and fluffy. Slowly add cooled melted chocolate, using a spatula as requred to scrape down the sides of the bowl. Add rum, and continue to beat until batter is somewhat thickened.
Transfer mixture to a bowl, cover with plastic wrap and refrigerate for 30-40 minutes, or until mixture is firm and well chilled.
Using a small cookie scoop, scoop a ball of the dough into your clean hand and form into a small ball. Roll in sprinkles and place on the prepared baking sheet. Continue until all the dough is used up.
Place baking sheet into the refrigerator to allow the balls to chill and firm up. Then, store between layers of waxed paper in an airtight continue for up to a week in the refrigerator or two months in the freezer.