In a medium saucepan, heat the olive oil and unsalted butter over medium heat until the butter melts.

Add the flour and cook, stirring constantly, for about 2 minutes until well combined.

Gradually stir in the milk and chicken broth (or vegetable broth).

Season with salt, black pepper, and nutmeg.

Continue cooking and stirring constantly until the mixture thickens and becomes smooth.

Add the finely chopped partridge (or quail), Serrano ham, cheese, and parsley.

Cook, stirring, for about 5 minutes.

Let the mixture cool slightly, stirring occasionally to release steam.

Spread the mixture out on a dinner plate and let it cool completely.

Refrigerate until firm enough to handle.

With floured hands, shape the partridge mixture into ½-inch balls.

Place the eggs and bread crumbs in separate shallow bowls.

Heat at least ½ inch of oil in a large skillet over medium-high heat (or use a deep fryer set at 365°F) until it turns a cube of bread light brown in 60 seconds.

Dip each croquette into the beaten eggs, dredge in the bread crumbs, and place in the hot oil.

Cook the croquettes, turning several times, until they become golden.

Transfer the fried croquettes with a slotted spoon to paper towels to drain.

Serve hot.