Warm the pot. Heat 2 tablespoons of olive oil in a large pot over medium heat until shimmering.
Sauté the aromatics. Add onion, carrots, and celery with a pinch of salt.
Cook 6–8 minutes, stirring, until the veggies are soft and lightly golden.
Add garlic and spices. Stir in garlic, red pepper flakes, dried thyme, and the bay leaf. Cook 30–60 seconds, just until fragrant.
Build the base. Add half the beans and all the broth. If using, drop in the Parmesan rind.
Bring to a gentle simmer.
Thicken naturally. In a bowl, mash the remaining beans with a fork. Stir them into the pot to give the soup body without cream.
Simmer. Let the soup bubble gently for 10–15 minutes to meld flavors. Taste and adjust salt and pepper.
Add the kale. Stir in the chopped kale.
Simmer 5–7 minutes, until tender but still bright green.
Finish with brightness. Remove the bay leaf (and Parmesan rind). Stir in the juice of half a lemon. Add more to taste if you like it zesty.
Garnish and serve. Ladle into bowls and top with chopped parsley.
Add a drizzle of olive oil and grated Parmesan if desired.