Add the sugar and water into a small saucepan over medium-low heat, stirring constantly until sugar is dissolved. Remove from heat and stir in the cocoa powder until dissolved. Let cool, and store in the refrigerator until ready to use.
For the cocktail
Add egg to the bottom of a shaker and use a barspoon or fork to break apart the yolk and the whites.
Add the chocolate syrup and the Cynar. Fill shaker with ice and shake vigorously for 10 seconds.
Double strain into a chilled coupe glass, top with bitters, and serve!