Coat bottom of a Dutch oven in thin layer olive oil and heat over medium-high flame.
Add the sausage and brown well on all sides, about 5 minutes. Don’t worry if the sausage isn’t cooked through in the center. After browning the sausage, remove it from the pot with a slotted spoon and set aside. (skip this step for veg)
Add the leek to the pot and reduce heat to medium. Sauté until leek starts to caramelize, about 10 minutes, then add the carrot. Cook together an additional 3 or so minutes, then add the broth to the pot. Cover and bring to a boil. Once carrots have softened a bit, stir in the kale and add the beans and sausage.
You can add parmesan rind (don't eat it), dash tamari, bay leaf for more flavor
Add seasonings. Return to a simmer and cook until the flavors meld together, about 15 minutes. Taste to correct seasonings and add more broth if you want it more soup-like.