Warm the olive oil in a large Dutch oven or soup pot over medium heat. Add the onion, carrots, and celery, then cook for 7–9 minutes, stirring occasionally, until the vegetables soften.

Add the minced garlic, Italian seasoning, and optional red-pepper flakes. Cook for 30–60 seconds, stirring constantly, just until the garlic is fragrant.

Stir in the tomatoes, broth, drained beans, Parmesan rind, kosher salt, and black pepper. Bring the mixture to a boil.

Reduce the heat and simmer the soup uncovered for 20–25 minutes. Stir occasionally so the beans and vegetables cook evenly and the flavors have time to come together.

For a thicker texture, mash about 1 cup of the beans against the side of the pot, or carefully blend 1–2 cups of soup and return it to the pot. This creates a creamy body without adding flour or cream.

Stir in the chopped kale and cook for 3–5 minutes, until tender. If using baby spinach instead, cook it for only 1–2 minutes.

Remove the Parmesan rind from the pot. Stir in the lemon juice or red-wine vinegar, taste the soup, and adjust the salt and pepper as needed.

Ladle the soup into bowls and finish with chopped parsley, grated Parmesan, and a small drizzle of olive oil. Serve immediately with crusty bread.