Pour the milk into a 1-pint canning jar. Stir in the brown sugar, cinnamon, and nutmeg.
Microwave, uncovered, for 1 minute. Cover the jar tightly with the lid. Wrap the jar with a kitchen towel or potholder and shake vigorously until foamy.
Pour the coffee into a large mug. Add the hot milk mixture. Spoon any remaining foam from the jar on top of the coffee. Sprinkle with cinnamon sugar.