Heat the 1/2 cup olive oil in a small saucepan over medium heat. Add the flour and cook for 3 minutes, stirring constantly. Very slowly add the milk, stirring constantly, and add the chicken broth until both liquids are incorporated. This can take up to 30 minutes.

Add the nutmeg and the salt and pepper. Cook over medium heat, stirring constantly until the sauce is thickened and smooth.

Add the minced ham and continue to cook for about 2 to 3 minutes over low heat, continuing to stir. Remove from heat. Taste and adjust seasoning if necessary.

Allow to cool for 5 to 10 minutes and then refrigerate at least for 3 hours until the mixture is cold. If you are preparing a day or so ahead, you can cover the mixture tightly and keep refrigerated until you are ready to fry the croquettes.

Beat the eggs with the water in a separate small, wide bowl.

Pour the breadcrumbs into a small, wide bowl.

Cover your hands in flour, then divide the mixture into 1-inch balls and set on a plate so that they are not touching.

Pour enough olive oil into a large frying pan to be 1/2-inch deep. Heat the olive oil to about 355 F.

Dip the croquettes in the beaten egg and coat with breadcrumbs by rolling in the bowl.

Place the croquettes in the hot oil and fry quickly, in batches, turning several times, until golden and all the croquettes are fried.

Remove the croquettes with a slotted spoon and set on a paper towel to absorb the excess oil. Serve immediately.