Melt butter in a saucepan over medium heat. Add onion and garlic, cooking until soft and translucent.
Gradually stir in flour to form a roux. Slowly add beef broth, stirring continuously to prevent lumps, until the mixture thickens.
Add shredded beef, nutmeg, salt, pepper, and parsley. Mix well and cook for 2-3 minutes. Remove from heat and let cool to room temperature.
Refrigerate the mixture for at least 3 hours until firm.
Shape the chilled mixture into small balls (about 1 tablespoon each).
In a small bowl, whisk eggs and milk together.
Dip each ball into the egg mixture, then roll in breadcrumbs to coat evenly.
Refrigerate the breaded balls for 1 hour.
Heat oil in a deep fryer or pot to 350°F (175°C).
Fry the Bitterballen in small batches for 3-5 minutes, or until golden brown.
Drain on paper towels and serve hot.