Combine beef, egg, breadcrumbs, onion, 3/4 teaspoon salt, and nutmeg in a large mixing bowl; mix well.
Shape into 1-inch meatballs.
Heat oil in a large heavy skillet; add meatballs, and brown on all sides.
Remove meatballs from pan; set aside.
Drain drippings, reserving 2 tablespoons in skillet.
Stir in cream cheese, milk, water, parsley, 1/8 teaspoon salt, and thyme into drippings; cook over medium heat, stirring constantly, until smooth and thickened.