Melt the butter and warm the oil in a heavy pan over medium high heat.
Add the diced onion and sauté for a few minutes, until it just starts to color.
Add a pinch of salt and the nutmeg. Don't add too much salt as the Serrano ham is already salty.
Add the diced ham and sauté for 30 seconds more.
Add the flour and stir continuously, until the flour turns a light brown color. You must not stop stirring or the flour will burn!
When the flour changes color, add the milk little by little, always stirring until you incorporate the entire amount. It should take about 15-20 minutes to add it all.
Turn off the heat and let the dough cool to room temperature.
Butter the sides of a large bowl and place the croquette dough inside, covered directly with plastic wrap. Refrigerate a minimum of 4 hours, but preferably overnight.
To make the ham croquettes, shape them into little logs (or use a pastry sleeve if you have one.)
Next, while heating a pan full of olive oil on the stove, pass the croquettes through the three step breading process. First, cover them in flour, then in egg, and, finally, in the breadcrumbs.
Fry the ham croquettes in the hot oil for about five minutes (making sure to turn halfway so they brown evenly) and then let them cool for a few minutes before enjoying!