1) In a large pot, cover the fennel, onion, and garlic with water and cook on medium high heat until the fennel is tender. This will take a while- taste the fennel leaves after the first half-hour (it will probably take 1-2 hours for this to occur- just keep an eye on it). The fennel greens should not be tough to chew. Depending on the amount of time it took to cook the fennel you may or may not want to add more water to the pot. It just depends on whether you want a thick heartier version or a lighter broth-like version. Either is good.
2) After the fennel has cooked,reduce to a simmer and add the tomato sauce, 1 tablespoon oil, and one chopped tomato. Also, add salt to taste. Add the chopped carrots next and cook until they are tender. Add cubed potatoes after the carrots have cooked and cook the cubed potatoes until tender. Lastly, add the can of drained dark kidney beans and let them heat thoroughly for just a few minutes.
A friend of mine made this for a potluck last spring and it's really great. The fennel does not overpower the flavors in the soup so for people skeptical of fennel this is for you! I made this for my southern cooking grandmother and she thought she could "make it better" by adding chicken stock to it- she called me after the fact and told me that she won't be doing that again.... apparently it's just not the same. :)