Cut an X in the base of each Brussels Sprout. Heat a large saucepan of water to a boil. Boil Brussels Sprout for 8 minutes. Drain. Let cool and then cut each Brussels Sprout in half.
In a medium saucepan over medium heat, melt butter. Stir in flour and cook for 1 minute. Add milk, stirring until sauce boils and thickens. Stir in Dijon mustard, salt, pepper and nutmeg. Remove from heat. Add ½ of the shredded cheddar cheese and stir until melted. Stir in Brussels Sprout.
Spoon mixture into a greased casserole dish. Sprinkle with remaining cheese. Bake for 30 minutes. Serve hot.