Melt 3 ½ tablespoons of butter In a pan over low heat. Add the flour a little at a time, stir and gradually add the milk, stirring constantly with a whisk. Cook over low heat until it begins to boil, add the salt and a pinch of nutmeg and remove from the heat.
In the meantime, cook the macaroni in a large quantity of lightly salted boiling water for the time indicated on the package. Drain the pasta and put it into a large bowl with the béchamel prepared as above.
Sprinkle with a couple of tablespoons of Parmigiano Reggiano and mix well. Butter a baking dish, pour in the macaroni and cover with the rest of the béchamel.
Dot with the remaining butter and bake in a preheated 350° oven for about 20 minutes or until the surface is golden-brown. Remove from the oven and serve immediately.