Make the chocolate syrup: Combine the sugar and 1/3 cup water in a small saucepan. Bring to a simmer over medium heat, then whisk in the cocoa powder until smooth. Remove from the heat and stir in the vanilla. Let cool completely.
Spoon about 2 1/2 tablespoons of the chocolate syrup into each glass. Add 1 1/2 cups milk and a generous pinch of salt. Stir until the syrup and salt dissolve.