Heat oil and butter in a large saucepan; add chopped onion, thyme and sausage chunks, browning over medium heat for about 10 minutes, adding a splash of wine for enhanced flavor. Drain off excess fat.
Add chopped kale, potatoes, garlic, cooking for a few minutes before adding chicken broth, bringing soup to a boil, then simmering for about 20 minutes.
To achieve a thicker consistency, strain out some of the cooked potato pieces, thoroughly mash and then add back to the soup.
Add cannellini beans and simmer for another 10 minutes, then serve!