Make the chocolate syrup: Bring the sugar and 1 1/2 cups water to a boil in a medium pot. Add the cocoa powder, vanilla and salt and whisk until well combined. Let cool completely.
For each drink, pour about 1 1/2 teaspoons of the chocolate syrup into a chilled shot glass and freeze until slightly firm, 5 to 10 minutes. Slowly pour the half-and-half on top of the chocolate syrup, then top with seltzer. Stir before drinking. (Refrigerate any leftover chocolate syrup for up to 6 months.)