In a medium saucepan, heat the unsalted butter and 5 tablespoons of olive oil over medium heat until the butter melts.

Add the flour and cook, stirring constantly, for about 3 minutes.

Gradually stir in the milk, chicken broth (or vegetable broth), salt, pepper, and nutmeg.

Continue cooking and stirring constantly until the sauce is thickened and smooth.

Add the finely chopped chicken and ham, and cook, stirring, until the sauce reaches the boiling point, approximately 10 minutes.

Let the mixture cool, cover, and refrigerate for at least 3 hours.

(The croquettes can be prepared up to this point and refrigerated for up to one day.

)

On a lightly floured work surface, shape the chicken mixture into 1-inch balls (about 1 tablespoon each) using floured hands.

Place the eggs and bread crumbs in separate shallow bowls.

Heat at least 1 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 egg, dredge in the bread crumbs, and place in the hot oil.

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

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

Serve hot.