Put the coffee, sugar and vanilla extract in a medium bowl and whisk until the sugar has completely dissolved. Pour the mixture into a 9-by-13-inch baking dish, cover with plastic wrap and freeze until completely solid, at least 6 hours and up to overnight.
When ready to serve, use a metal fork to scrape the frozen coffee mixture into fine shavings. Scoop the shavings into small serving bowls or snow cone cups. Serve frozen.
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