Heat 2 1/2 cups milk in a saucepan over medium heat until steaming, about 5 minutes. Stir in brown sugar, maple syrup, honey, and vanilla extract. Bring to boil and stir in cocoa powder. Remove from heat and add the remaining 1/2 cup milk. Return saucepan over heat and simmer until heated through, about 2 minutes more. Ladle into cups to serve.