Make cream soda ice cubes. Before getting started on the recipe you'll need to freeze 2 bottles or 24 ounces of cream soda to make cream soda ice cubes.
Melt the brown sugar. In a small saucepan set over medium heat, blend together the brown sugar and water. If you have one, attach a candy thermometer to the side (optional) and continue to stir the mixture as it comes to a boil. Once it reaches 240º F or reaches a vigorous rolling boil, typically taking about 5 minutes, lower the heat to a gentle simmer.
Add the final brown sugar mix ingredients. Incorporate the butter, salt, and cider vinegar into the melted brown sugar mixture. Continue to stir until the butter is entirely melted, and all the ingredients are thoroughly blended. Remove the mixture from the heat source and gently fold in the rum extract. Allow the mixture to cool down entirely.
Blend the cream soda. Place 1 tray of cream soda ice cubes into a blender along with 12 ounces of cream soda. Blend until it's thick and frothy.
Arrange. Add 2 to 3 tablespoons (or adjust to your preference) of the brown sugar base mixture into the bottom of each glass. Next, pour in cream soda, filling the glass to approximately 3/4 full, and then stir the contents together.
Make the whipped topping. Using an electric mixer or a handheld mixer and a medium bowl, whisk together 2 tablespoons of the brown sugar mixture and the heavy cream until it thickens and begins to form soft peaks.
Garnish. Spoon the whipped topping onto each glass.