Mix together the ground meat, onions (pulverized), eggs, milk, bread crumbs and all of the spices except the whole allspice.
Roll the meat mixture into half inch round balls - should be enough to cover about 3 baking sheets (sheets used solely to hold the rolled meatballs while they're waiting to be browned).
Brown the meatballs in butter: place a large pan over medium to high heat and combine 1 TBS of butter with a half a baking sheet worth of meatball at a time for a total of six batches. Place the browned meatballs into baking dishes - two large baking dishes should be sufficient.
Keep the heat on medium high and add the beef broth. Bring to a simmer.
Once the mixture has thickened to a gravy, add salt and pepper to taste, and then pour over the meatballs.
Sprinkle the whole allspice evenly among the meatballs.
Bake the meatballs for 45-60 minutes at 350 degrees.