Melt the 2 tbsp of oil and the butter in a pot and then over a low flame, add the flour, mixing well with a wooden spoon to form a roux. When the roux turns yellows slowly add the cold milk (always stirring), a little salt and a pinch of nutmeg. Let everything thicken over a low heat, stirring constantly with the wooden spoon to avoid lumps. Continue stirring until the roux leaves the sides of the pot (nowadays, cooks use hand mixers or beaters). While stirring add the pieces of ham so they are incorporated throughout the roux by the stirring.
Let it stand at least 2 hours until it cools.
Once the roux is cold, make the croquettes using a tablespoon to take the portion from the pot and shape it with your hands.
Place the 2 well beaten eggs in a bowl and in another bowl place the finely grated bread.
Coat each croquette with the bread crumbs, then dip into the eggs and again into the grated bread and fry them in very hot and deep oil (6 pieces at a time). Let them rest on paper serviettes to drain off the oil.