In a medium saucepan, melt the butter over medium heat. Add the finely chopped onion and sauté for 3 to 4 minutes until translucent and softened.

Whisk in the half cup of flour to create a roux, cooking for 2 minutes until it becomes light golden and smells nutty. Gradually whisk in the beef broth until you have a smooth, very thick gravy.

Stir in the finely shredded beef, fresh parsley, salt, black pepper, and nutmeg. Cook for another 2 minutes until the mixture pulls away from the sides of the pan.

Transfer the beef mixture to a shallow dish, cover tightly with plastic wrap, and refrigerate for at least 3 hours until completely firm. Chilling is crucial so the mixture holds its shape during frying.

Once firm, scoop out tablespoon-sized portions of the chilled beef mixture. Roll them into smooth balls using your hands.

Set up a breading station with three shallow bowls containing the remaining flour, beaten eggs, and breadcrumbs. Roll each ball in the flour, dip into the egg, and coat thoroughly in the breadcrumbs.

Heat the vegetable oil in a deep, heavy-bottomed pot to 350 degrees Fahrenheit. Carefully fry the bitterballen in batches of 5 to 6 for 4 to 5 minutes until perfectly golden brown and crispy.

Use a slotted spoon to transfer the fried bitterballen to a paper towel-lined plate to drain excess oil. Serve immediately with a side of grainy Dijon mustard for dipping.