Step 1In a 5-quart heavy-bottom pot, melt the butter over medium-high heat. Stir in the potato, leek and all but 2 cups each of the onion and celery and cook, stirring frequently, until the onion just begins to color, about 10 to 12 minutes.
Step 2Add the canned tomatoes, plum tomatoes and brown sugar, stirring to crush the tomatoes and scrape any flavoring from the bottom of the pan.
Step 3Stir in the oregano, basil and vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Loosely cover the pan and continue to simmer until the vegetables break down and the soup begins to thicken, about 45 minutes. Remove from heat and puree the soup using an immersion blender, or in batches using a regular blender. Taste and season with 1 teaspoon salt and several grinds of black pepper, or as desired (the salt content of vegetable broth will vary by brand).
Step 4Stir in the carrot, fennel and remaining onion and celery. Continue to simmer gently until the vegetables are tender, 20 to 25 minutes, stirring frequently. About 10 minutes before the vegetables are tender, stir in the beans to warm. Taste and adjust the seasoning as desired.
Step 5This makes about 4 quarts soup, and will keep for up to 1 week, covered and refrigerated.