Make the cold brew coffee: Stir coarse ground coffee into cold water. Cover and refrigerate for 18 - 24 hours. Strain through cheesecloth and store the coffee in a clean jar or pitcher, covered, in the fridge until ready to use. It should last up to 2 weeks.
Set aside 1 teaspoon of the caramel. Stir the remaining caramel sauce into the cold brew until combined.
In a French press, or blender, add the half-and-half, remaining caramel, vanilla syrup and salt. Plunge up and down to create cold foam, or briefly pulse the blender to create foam.
Add ice to a glass with the caramel coffee and spoon on some cold foam. It will swirl down into the coffee.
Notes
You can make the caramel coffee ahead of time, but for best results, the cold foam needs to be made just before serving.Switch the vanilla syrup for other flavored syrups, such as Biscoff Syrup, Chai Syrup, or Rose Syrup.Instead of cold brew coffee, you can use cold regular coffee.Try it with a decaf cold brew if you don't want that coffee rush!