In a small saucepan, whisk the sugar, cocoa powder and salt until evenly combined, then whisk in the water.
Bring to a gentle simmer over medium-low heat, whisking, for 2 to 3 minutes, until the sugar dissolves and the syrup is smooth.
Remove from heat. Stir in the vanilla extract and 1/2 teaspoon peppermint extract. Taste, then add more peppermint if you'd like, up to 3/4 teaspoon total. Let cool.
Whisk in the heavy whipping cream (or half-and-half).
Transfer to a clean jar, seal and refrigerate promptly. Shake before using and stir into coffee to taste.
Refrigerate. Will last until expiration date on heavy whipping cream.