Place a large pot on high, allow to heat.
Add oil and then sausage to pan pressing it into the bottom of the pan. You want to allow it to brown in one big, even, flat mass. Be patient, this will likely take 5-7 minutes.
Break sausage up into large chunks, add all the peppers, carrots and onion, cook on medium with lid on, allowing the vegetables to brown and soften, season with salt and pepper. Cook 5-10 minutes.
Deglaze with wine, scraping all the brown bits up with a wooden spoon.
Add stock and canned tomatoes and reduce.
Add kale, return lid and allow to wilt about 2 minutes.
Add canned beans and simmer 1-2 minutes more.
Lastly finish with basil and olive oil to your liking.