In a saucepan, melt butter at medium-low heat. Add onion and cook for 1 minute. Slowly whisk in milk, 1/3 cup of flour, nutmeg, salt, and pepper. Continue to whisk until it becomes thick.
Add in the cooking wine and ground ham to the sauce. Mix together slowly until all is combined. Reduce heat to low and let simmer for 5 minutes.
Transfer the filling to a bowl. Let it rest at room temperature then refrigerate for 2 hours or overnight (the longer the better).
Remove the filling from the refrigerator. Form logs then place them back in the fridge to firm up once again, about 30 minutes.
Dip each log in the egg wash then coat in breadcrumbs. Let the croquettes rest at room temperature for 5 minutes before frying.
In a large pot, heat enough vegetable oil to cover the croquettes completely. Fry each croquette until golden brown, approximately 3-4 minutes. Drain, serve and enjoy!