Combine the roughly chopped tomatoes, fennel stems, roughly chopped onion, and minced garlic in a large pot over high heat, season with salt and pepper, and cover. The liquid released from the vegetables as they are heated makes oil unnecessary. Keep an eye on them as they cook for 25 to 30 minutes, or until the vegetables are tender, stirring occasionally.
Add the chicken stock and simmer for about 15 minutes. Puree with a hand-held blender or in a blender or food processor for about 30 seconds. Add the basil and process until the mixture is smooth but still a bit thick. Strain through a medium sieve, pushing through excess pulp but discarding large pieces of tomato skin.
Place the diced tomato, fennel bulb, diced onion, and sliced garlic in a large soup pot and cook over medium high heat, stirring occasionally, for about 10 to 12 minutes, or until vegetables are tender. Add the strained liquid, bring to a simmer, and adjust the salt and pepper.
Recipe courtesy of Commander's Kitchen (Broadway, 2000) by Ti Adelaide Martin and Jamie Shannon