Sift cocoa into medium bowl. Brin cream and ground coffee to boil in heavy small saucepan, stirring to blend. Remove from heat; cover and steep 10 minutes.
Strain cream through fine sieve into another bowl, pressing on coffee grounds to release as much cream as possible.
Bring sugar, corn syrup, 1/4 cup water, and coffe-flavored cream to boil in medium saucepan; whisking until sugar dissolves. Boil 1 minute, brushing down sides of pan with wet pastry brush. Remove from heat.
Whisk in chocolate, butter and vanilla. Pour 1/4 of chocolate mixture into cocoa to moisten, then add remiaing chocolate mixture, whisking until sauce in smooth and shiny.
Cool. COver and refrigerate. Rewarm sauce over low heat before serving.