Heat oven to 350° F. In a medium skillet, over medium heat, heat the oil with the onion, celery, and garlic, and cook until the vegetables are tender but not browned, about 10 minutes. Add 2 teaspoons salt, allspice, and nutmeg. Remove from heat.
In a large bowl, whisk the eggs, then blend in the milk and bread crumbs. Add the meat and cooked vegetables and stir or work with your hands to combine. Shape into 1-inch balls. Sauté over medium-high heat, in tablespoon olive oil, a few meatballs at a time, removing them when well browned on all sides. Pour off all but 2 tablespoons of the fat. Whisk in flour, 1 teaspoon salt, sugar, and a few grinds of black pepper. Cook over medium heat, scraping up any browned bits. Whisk in light cream and water. Bring to a boil, stirring constantly, until the sauce thickens, at least 1 minute. Return the meatballs to the skillet and simmer over low heat for 20 minutes.