- Preheat oven to 375 degrees. Grease 6-inch cake pan.
- Combine cola, butter, and marshmallows in saucepan over medium heat and stir until smooth. Set aside.
- Sift dry ingredients together into mixer with paddle attachment. While on low speed, add cola mixture to dry ingredients. Add eggs and extract.
- Turn off and scrape down sides of mixer. Turn back on low speed and gradually add buttermilk and mix until smooth. Pour into pre-greased cake pan and bake at 375 degrees for 45 minutes to 1 hour until set.
- Place on cooling rack until cool enough to handle. Once no longer warm, wrap and place in refrigerator and allow to cool overnight.
- After cake has rested overnight, unwrap it and tear it into small pieces and spread out evenly over an unsprayed baking sheet pan. Bake cake pieces at 300 degrees for 20 minutes. Pull out pan, stir, and break up cake and place back in oven for additional 25 minutes. Cool cake completely. Once cake is room temperature, pulse the dried-out cake pieces in food processor to get uniform crumbs.
- Line baking sheet with parchment paper. In mixer with paddle attachment, combine butter and cream cheese. Paddle 2 – 3 minutes on medium.
- Add powdered sugar, cocoa, and lime zest. Add cola and rum. Continue mixing until smooth. Once completely smooth, add cake crumbs and mix until evenly coated.
- Scoop mixture into balls with tablespoon onto lined baking sheet. Roll balls smooth in hands and place in refrigerator for 30 minutes.
- Place lollipop sticks in center of each ball. Chill in freezer for an additional 30 minutes.
- Melt dipping chocolate and dip each ball quickly in chocolate and spin off any excess chocolate. Before chocolate sets, sprinkle with candied ginger pieces. Let chocolate set and serve.