Whisk together whole egg, 1/4 cup brown sugar, cocoa and the infused milk in another saucepan until smooth. Cook over low heat, whisking constantly, until thickened, about 5 minutes. Remove from the heat and add the softened gelatin mixture, stirring until the gelatin has dissolved. Add chocolate and vanilla; stir until the chocolate has melted. Set aside to cool to room temperature, about 30 minutes.