Melt 50g unsalted butter in a heavy-based saucepan over medium heat. Add 60g plain flour all at once, stirring constantly to form a golden roux, about 2 minutes.
Remove from the heat and gradually whisk in 500ml warmed whole milk, beating well to avoid lumps. Return to medium–low heat and cook the béchamel sauce, stirring continuously, until it thickens and starts to pull away from the sides of the pan, 10–15 minutes.
Stir in 100g finely chopped Serrano or Iberico ham, a pinch of freshly grated nutmeg, and season with salt and freshly ground black pepper. Mix thoroughly and adjust the seasoning to taste.
Spread the mixture onto a tray and cover with cling film pressed directly onto the surface. Chill for at least 4 hours, ideally overnight.
Shape the chilled mixture into small logs or balls, dip them into the beaten eggs, then coat evenly in the breadcrumbs. Heat enough extra virgin olive oil in a deep frying pan or deep-fat fryer to 180°C (if using a thermometer) and fry the croquettes in batches until golden brown. Drain on kitchen paper and serve hot.