Make the Béchamel:

In a saucepan over medium heat, melt the butter with the olive oil. Add the 1/2 cup flour and stir continuously to create a roux. Cook for a couple of minutes without letting it color.

Incorporate Milk:

Gradually add the milk, stirring constantly to prevent lumps, until you have a smooth, thick béchamel sauce.

Add Ham and Season:

Mix in the chopped ham, season with salt, white pepper, and a pinch of nutmeg. Cook for another minute.

Cool the Mixture:

Spread the mixture onto a plate and cover with plastic wrap directly on the surface to prevent a skin from forming. Chill in the refrigerator until firm, at least 2 hours.

Shape the Croquettes:

Once chilled and firm, shape the mixture into small cylinders.

Bread the Croquettes:

Roll the croquettes in flour, then dip into the beaten eggs, and finally coat with breadcrumbs.

Fry the Croquettes:

Heat oil in a deep fryer or a deep skillet to 350°F (175°C). Fry the croquettes in batches, turning occasionally, until golden brown. Remove with a slotted spoon and drain on paper towels.

Serve:

Serve the croquettes hot as an appetizer or with a light salad for a meal.