Place cocoa powder and salt in the bowl of a food processor and pulse to break up lumps.
Bring the water, sugar, and corn syrup to a boil over medium heat in a small saucepan.
Turn the food processor on and let it run continuously while carefully pouring the boiling-hot sugar mixture into the feed tube. Add the vanilla and cardamom.
Let cool 15 minutes and then funnel into a squeeze bottle. Serve immediately or store in the refrigerator until ready to use.