1. In a small saucepan, combine brown sugar with 2 tablespoons water. Bring to a boil over medium heat and cook until the mixture reaches 240 degrees, stirring occasionally which is about a minute of cooking. Turn off the heat and add the butter, salt, vinegar, and 1/4 cup heavy cream. Stir until smooth. Cool mixture to room temperature before using.
2. In a medium bowl, beat together the remaining cream (1/2 cup) with 2 tablespoons of the brown sugar syrup.
3. In each glass, mix together 1/4 cup brown sugar syrup with 1/4 cup cream soda. Pour in the rest of the cream soda until it is nearly to the brim of the glass. Top with whipped cream.