Cinnamon is known as a sweet spice, but it can have a pungent bite. Vietnamese cinnamon, also known as Saigon cinnamon, is an especially fragrant variety, and its taste is sharper than that of regular cinnamon. It is worth seeking out.
In a glass measuring cup, pour the boiling water over the espresso. Cover the measuring cup with a small plate and let steep for 10 minutes. Strain the espresso through a paper filter into a small saucepan.
Whisk 1/4 cup of the sugar and 1 teaspoon of the cinnamon into the espresso and bring to a boil. Reduce the heat to moderate and simmer for 1 minute. Remove the saucepan from the heat, add the chocolate and, using a wooden spoon, stir until smooth. Using a rubber spatula, scrape the mocha mixture into a small bowl and let cool to room temperature, stirring a few times.
Meanwhile, in a large bowl, whip the heavy cream with the remaining 1 1/2 tablespoons of sugar and the vanilla until the cream holds soft peaks. Add the cooled mocha mixture and whip until the cream holds firm peaks. Cover the mocha cream and freeze until set, about 3 hours.
Using a medium ice cream scoop, add 3 or 4 small scoops of the frozen cream to tall soda glasses. Add club soda and sprinkle cinnamon over the top. Serve at once with a straw and a long-handled spoon.
Make Ahead: The mocha cream can be frozen for up to 2 days. Let it stand at room temperature for about 10 minutes before scooping.
Notes: Vietnamese cinnamon is available by mail order from Penzeys Spices, 800-741-