Mix cream, sugar, cocoa, corn syrup, and salt in a medium saucepan. Bring to a boil over medium-high heat and cook just until sugar has completely dissolved, about 3 minutes. Remove from heat.
Add chocolates and vanilla and stir until chocolate is melted and sauce is completely smooth. If you have any lumps, gently press and smear them against the bottom of the pan with a spatula as you stir.