1) In the base of a cocktail shaker, mix together espresso and sugar until sugar is dissolved. Fill shaker with crushed ice, close, and shake until shaker is frosted and mixture is foamy, about 20 seconds.
2) Strain into a martini glass, top with a dollop of coffee whipped cream, and serve.
For the coffee whipped cream:
1) Place very clean glass or metal bowl and metal whisk in freezer just until cold, about 5 minutes.
2) When everything is cold, place cream in bowl and begin to whisk until it froths up and starts to thicken, about 1 minute. Whisk vigorously until soft peaks form (the cream will hold a point when the whisk is lifted but will fall back into the bowl almost immediately), about 1 minute.
3) Add the liqueur and whisk until stiff peaks just form (the cream stays put on the whisk when it is lifted from the bowl), about 1 minute. Store covered in refrigerator until ready to use.