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 the 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 1 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 1/4 cup all-purpose flour, 1 teaspoon salt, 1 teaspoon sugar, and a few grinds of black pepper. Cook over medium heat, scraping up any browned bits. Whisk in 1 3/4 cups light cream and 1 cup 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.
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