Heat 2 tablespoons oil in a 5 to 6 quart pot over high heat until hot but not smoking, then cook onions, garlic, celery and carrots, stirring occasionally, until onions are pale golden, about 4 minutes.

Stir in broth and water and bring to a boil, covered

Meanwhile, heat remaining 2 tablespoons oil in a 12-inch heavy skillet over high heat until hot but not smoking, and sauteing meatballs, do not thaw if frozen, turning occasionally, until browned all over, about 3 minutes.

Add meatballs to soup along with beans, and briskly simmer, covered, stirring occasionally, until vegetables are tender and meatballs are heated through, about 15 minutes.

Stir in spinach, cheese, salt and pepper and simmer, uncovered until spinach is wilted, about 1 minute.

Top with more finely grated cheese if desired.