1. Combine the baked beans, water, onion slices, and celery in a large heavy saucepan (at least 4 qt / 3.8 L capacity). Bring to a simmer over medium heat.
2. Simmer uncovered for 30 minutes, until the beans are very soft and the celery is completely tender and the broth is lightly flavored throughout.
3. Remove from heat. Working in batches if needed, press the soup through a fine-mesh sieve or food mill, discarding solids. Return the strained soup to the saucepan.
4. Stir in the stewed and strained tomatoes and the chili sauce. Return the soup to low heat.
5. Prepare a beurre manié (a technique for thickening sauces): mash the butter and flour together with a fork until a smooth paste forms. This raw paste will cook out in the soup, thickening it without lumps.
6. Whisk the butter-flour paste into the simmering soup a small piece at a time. Continue to simmer, stirring frequently, for 5–8 minutes, until the soup is noticeably thickened and no floury taste remains.
7. Season to taste with salt and pepper. Serve hot in warmed bowls.
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