In a medium bowl, combine eggs, fat, 1 1/2 tsp. salt, nutmeg, and 1/8 tsp. pepper. Stir in matzo meal until well blended. Add 3 tbsp. water, parsley, and onion; mix well. Cover and chill for about 20 minutes.
In a medium saucepan, bring broth to a boil over high heat. Using your hands, shape rounded tablespoonfuls of matzo mixture (it will stick slightly) into balls and drop into the boiling broth. Reduce heat, cover, and simmer gently until the matzo balls are spongy and light in the center (cut into 1 to test), about 30 minutes. Season soup to taste with additional salt and pepper.
With a slotted spoon, lift matzo balls to serving bowls or a tureen. Pour hot broth over them.