Heat a large Dutch oven or soup pot over medium-high heat. Add the sausage, using the olive oil only if the sausage is lean, and cook for 6–8 minutes while breaking it into small pieces until browned and no longer pink. Drain excess fat if necessary.

Add the diced onion, sliced carrots, and celery to the browned sausage. Cook for 5–7 minutes, stirring occasionally, until the vegetables begin to soften and pick up the savory browned bits from the bottom of the pot.

Stir in the minced garlic and crushed red-pepper flakes. Cook for about 30 seconds, just until the garlic is fragrant and the pepper flakes begin to perfume the pot.

Add the diced tomatoes with their juices, broth, drained beans, Italian seasoning, kosher salt, and black pepper. Stir well, then bring the soup to a boil.

Reduce the heat to maintain a gentle simmer, partially cover the pot, and cook for 15–20 minutes. The soup is ready for the next stage when the carrots and celery are tender when pierced with a fork.

Add the sliced zucchini and simmer for 5–7 minutes more. This timing keeps the zucchini tender while helping it retain a pleasant shape and fresh flavor.

Stir in the chopped kale or baby spinach during the final 1–2 minutes. Cook only until the greens are wilted, then taste and adjust the salt, pepper, and red-pepper flakes before serving hot.