In a small bowl, combine coffee grounds, cinnamon and nutmeg; pour into a coffee filter of a drip coffeemaker. Add the water; brew according to the manufacturer's directions.
In a large saucepan, combine the milk, chocolate syrup and brown sugar. Cook over low heat until sugar is dissolved, stirring occasionally. Stir in the vanilla and brewed coffee. Ladle into mugs; garnish with whipped cream if desired.