Heat olive oil in a large, heavy pot over medium-high heat. Stir in onion; cook for 2 minutes, stirring occasionally. Stir in garlic, Italian herbs, and crushed red pepper; cook for 30 seconds more. Stir in vinegar and cook until it evaporates, about 30 seconds.
Stir in broth, tomatoes (with liquid), water, and rice. Bring to a boil over high heat. Cover and cook over medium heat for 30-40 minutes.
Stir in beans and olives. Cover and cook until rice is tender, 8–10 minutes longer. Stir in spinach, red bell pepper, and salt to taste. Cook over medium heat, uncovered, until spinach is tender, about 1 minute.
Turn off heat. Stir in salt, black pepper, and rosemary to taste.