Combine brown sugar and water in a small saucepan; bring to a gentle boil and cook stirring often until reads 240 degrees on a candy thermometer.
Stir in the butter, salt, vinegar and 1/4 cup of heavy cream; set aside to cool to room temperature.
Once it is cool, stir in the extract.
Combine 2 tablespoons of the sugar mixture and the remaining 1/2 cup of heavy cream; beat with an electric mixer 2 or 3 minutes until just thickened but not completely whipped.
To serve, divide the brown sugar mixture between 4 tall glasses (about 1/4 cup each).
Add 1/4 cup of cream soda to each glass, stirring to combine.
Fill each glass nearly to the top with the additional soda.