Add coconut milk, brown sugar cane and salt to medium saucepan over medium heat. Whisk until sugar dissolves and milk comes to simmer, about 5 minutes.
Reduce heat to medium low. Whisk in cocoa powder and bittersweet chocolate. Cook, whisking constantly, until cocoa powder and chocolate dissolve and mixture is smooth and thick, about 5 minutes more. Whisk in vanilla extract.
Divide hot chocolate evenly among serving mugs. Top with whipped cream and shredded coconut, if desired.