Combine the balsamic vinegar, salt, and brown sugar in a saucepan over medium-high heat. Heat until the sugar dissolves. Set aside and allow to fully cool.
In a blender, add the strawberries and banana and blend until smooth.
Add the balsamic sugar mixture and blend.
Add the ice cream and heavy cream. Serve in a cup and top with whipped cream.
Notes
If the milkshake is too thick, add additional heavy cream.