1. Preheat oven to 400 degree F. Spray two 15x10x1-inch jelly-roll pans with vegetable cooking spray.
2. Melt 2 tablespoons of the butter in a large skillet over medium heat. Add the onions and cook about 8 minutes or until tender. Transfer to a large bowl and cool.
3. Soak the bread cubes in the milk in a small bowl 1 minute, then squeeze very dry, discarding milk. Add bread to onions with the beef, eggs, salt, nutmeg, fines herbs, paprika, mustard, and pepper; mix well. Shape into forty 1-1/2 inch balls. Arrange on the prepared jelly-roll pans. Bake for 18 to 20 minutes, turning meatballs once and rotating pans halfway through. Remove meatballs from pans and set aside.
4. Pour 2 tablespoons of water into each jelly-roll pan, scraping up browned bits from bottom. Heat the remaining 2 tablespoons of butter in a large skillet over medium heat. Add the garlic and cook 30 seconds. Stir in the flour and tomato paste and cook 1 minute. Whisk in the beef broth, water, and drippings from jelly-roll pans. Bring to a boil. Add meatballs to skillet. Sprinkle with dill. Makes 40 meatballs.