Combine the sugar, water, and cocoa in a medium saucepan and bring to a boil, stirring to dissolve the sugar. Cook until the syrup is clear.

Remove from the heat and stir in the espresso and vanilla.

Let cool to room temperature. Transfer to a container, cover, and refrigerate until thoroughly chilled, about 3 hours.

Pour into a 9-inch nonreactive square pan, cover with aluminum foil or plastic wrap, and place in the freezer.

Once an hour, stir with a fork, scraping the crystals from the sides of the pan into the liquid center.

Repeat 2 or 3 times until the entire mass is set into small, light crystals, 2 to 3 hours.

Serve at once or transfer to a container, cover, and freeze.

To serve, spoon into chilled parfait or other decorative glasses, letting it mound on the surface, and pour 1 teaspoon of brandy over each serving.

Top with whipped cream, if desired.