In small saucepan, add 2 cups of milk and ¼ teaspoon salt. Whisk together and heat mixture until just boiling, stirring constantly. Once boiling, remove the saucepan from the heat and set aside.
In heavy-bottomed saucepan, melt 2 tablespoons of butter over low heat. Once melted, blend in the flour and cook slowly over low heat, stirring continuously until mixture becomes a white roux, without any browning.
Next, remove saucepan from heat. When roux stops bubbling, pour in all of the hot milk and begin whisking roux and milk vigorously. Be sure to get all roux from sides, bottom, and edges of saucepan.
Once combined, return saucepan to heat and raise heat to medium. Stir until sauce starts to boil. Boil mixture, still stirring, for 1 minute. Remove saucepan from heat and add additional salt and pepper to taste. Whisk in grated cheese until cheeses are completely melted and blended into sauce completely.
Season with nutmeg and additional salt and pepper, if needed. Stir in 2 tablespoons butter until butter is completely melted and sauce is well-blended. Serve sauce warm.
Enjoy with au gratin dishes, macaroni and cheese, Truly delicious!