Preheat oven to 180°C. Brush the base and halfway up the sides of a 1.5L (6-cup) capacity baking dish with butter to lightly grease.
Cook baby Brussels sprouts in a saucepan of salted boiling water for 2 minutes or until bright green and tender crisp. Drain. Transfer to the prepared dish.
Place the milk in a small saucepan over medium heat. Bring to a simmer. Remove from heat.
Melt the butter in a saucepan over medium-high heat until foaming. Add the flour and cook, stirring, for 1-2 minutes or until the mixture bubbles and begins to come away from the side of the pan. Remove from heat. Gradually add half the milk, whisking constantly with a balloon whisk until smooth. Gradually whisk in the remaining milk. Place the pan over medium-high heat and bring to the boil, stirring constantly with a wooden spoon, for 3 minutes or until the sauce thickens. Stir in the mozzarella.
Season with salt, white pepper and nutmeg. Pour the sauce over the Brussels sprouts. Season with salt. Bake for 10 minutes or until golden.