In a saucepan, over medium heat, add butter, chocolate, and cola. Bring mixture to a boil and remove from heat. Add in marshmallows and stir until melted. If the mixture cools too much so marshmallows don't completely melt, return to the heat and continue stirring. Set aside to cool.
Preheat oven to 350°. Grease or spray a 11x8x2-inch baking pan (can use a 9×13-inch but cake will be thinner). Place a piece of parchment paper in the bottom and up the ends of the pan. It should be cut to fit the bottom of the pan and extend about 4-inches up each end of the pan. Lightly spray with baking spray.
In a large mixing bowl, add vanilla, oil, and sugar and mix until smooth. Add eggs and buttermilk and combine until thoroughly incorporated.
In a separate bowl, combine flour, baking soda, baking powder, salt, and cocoa.
Add half of the dry mixture to the wet mixture and mix, scraping bowl as you do so. Add the cola mixture, combine, then add the remaining half of the dry mixture, mixing well.
Pour batter into pan and bake on the middle rack of the oven for approx. 50 min. or until the toothpick inserted into the center comes out clean.
Remove from oven and allow to cool for about 30-minutes. Using parchment paper to lift the cake, remove the cake to a cooling rack and finish cooling completely.
In a medium mixing bowl, combine cream cheese and softened butter until light and fluffy. Mix in vanilla. Gradually add powdered sugar, continuing to mix. If icing is too thin, you can either add in more powdered sugar or chill the icing for about an hour if you don’t want to add more sugar.
Spread icing onto cooled cake. Sprinkle chocolate curls over icing