bring a lrg pot salted water to boil.add the brussel sprouts and cook 7 minutes. drop into a bowl ice water to stop cooking process
make sauce by by melting the butter and flour and mix and cook stirring about 1 minute. slowly whisk in the milk and continue to cook, stirring frequantly until creamy 3 minutes. add 1/3 of american cheese and stir until melted smooth mix with salt and pepper to taste.
nalve the brussel sprouts through core and put in even layer in a 2 quart baking dish. pour the sauce over the sprouts and top with remaining cheese bake in center oven until golden brown on top 15 to 20 minutes. serve