Melt butter in a medium saucepan over medium-low heat.
Add brown sugar, salt, and vanilla extract. Whisk to combine.
Cook mixture for 5 minutes, or until brown sugar is completely dissolved.
Whisk in heavy cream and continue to cook for 1 minute.
Allow mixture to cool to room temperature (about 15 minutes).
Divide between 4 large glasses filled halfway with ice.
Slowly top with soda, being careful not to overfill. Stir to blend.