In a small saucepan over medium, combine the brown sugar and water. Bring to a gentle boil and cook, stirring often, until the mixture reads 240 F on a candy thermometer.

Stir in the butter, salt, vinegar and 1/4 heavy cream. Set aside to cool to room temperature.

Once the mixture has cooled, stir in the rum extract.

In a medium bowl, combine 2 tablespoons of the brown sugar mixture and the remaining 1/2 cup of heavy cream. Use an electric mixer to beat until just thickened, but not completely whipped, about 2 to 3 minutes.

To serve, divide the brown sugar mixture between 4 tall glasses (about 1/4 cup for each glass). Add 1/4 cup of cream soda to each glass, then stir to combine. Fill each glass nearly to the top with additional cream soda, then spoon the whipped topping over each.