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1
Combine the sugar, water, and cocoa in a medium saucepan and bring to a boil, stirring to dissolve the sugar.
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2
Cook until the syrup is clear.
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3
Remove from the heat and stir in the espresso and vanilla.
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4
Let cool to room temperature.
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5
Transfer to a container, cover, and refrigerate until thoroughly chilled, about 3 hours.
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6
Pour into a 9-inch nonreactive square pan, cover with aluminum foil or plastic wrap, and place in the freezer.
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7
Once an hour, stir with a fork, scraping the crystals from the sides of the pan into the liquid center.
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8
Repeat 2 or 3 times until the entire mass is set into small, light crystals, 2 to 3 hours.
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9
Serve at once or transfer to a container, cover, and freeze.
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10
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.
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11
Top with whipped cream, if desired.
