Start by muddling the blackberries in the bottom of your cocktail shaker.
This will release the juice and flavor from the berries.
Add the Cognac, Cointreau, and freshly squeezed lemon juice to the shaker.
Fill the shaker with ice and shake the mixture vigorously for about 30 seconds.
Prepare your serving glass by dipping the rim in lemon juice and coating it with sugar.
This adds a sweet touch to each sip.
Strain the cocktail mixture into your prepared glass.
Garnish with a skewer of blackberries and a sprig of thyme, if you like.
Serve immediately.