Light a grill for direct medium heat, to about 350 degrees.
While the grill preheats, combine the milk chocolate and milk in a small saucepan. Heat over low heat until the chocolate has melted. Whisk in the espresso power until fully dissolved and smooth. Stir in vanilla.
Grill donuts covered until lightly browned, about 1 minute. Serve with warm Mocha Dunk.