In a medium saucepan, warm oil and melt butter at medium-low heat. Add flour and cook for 1-2 minutes. Slowly whisk in milk, nutmeg, and pepper. Continue to whisk until it becomes a thick sauce (a roux), 2-3 minutes. Mix in the ham, cheese and chives and continue to cook 2-3 minutes; stirring until mixture is well combined. If mixture is too dry, add a splash more of milk.
Transfer the mixture to an 8x8-inch baking pan and spread out evenly. Let the mixture cool at room temperature, then cover and refrigerate overnight.
When ready to cook, remove filling from refrigerator. Shape mixture into approximately 2-inch balls.
In a bowl, whisk eggs and set aside. In another bowl, mix in the bread crumbs. Dip each croquette in the egg wash and then coat in panko. Transfer shaped croquettes back to refrigerator and chill 15-20 minutes.
Meanwhile to make aioli, mix all ingredients in a small bowl and combine until smooth. Set aside.
In a large pan, heat enough vegetable oil to cover the croquettes completely. Working in batches, fry each croquette until golden brown, approximately 3-4 minutes.
Transfer croquettes to a paper towel lined plate to dry briefly. Serve immediately with paprika aioli. Enjoy!