Drain one can of tomatoes, discarding juice, then purée with remaining (undrained) can tomatoes in a blender.
Cook onion, garlic, jalapeño, and ginger in oil in a 4- to 5-quart heavy, nonreactive pot over medium heat, stirring frequently, until onion is softened (about 8 minutes).
Add cumin and cook, stirring for one minute.
Stir in puréed tomatoes, broth, sugar, and salt and simmer, uncovered, stirring occasionally for 20 minutes.
With an immersion blender, or working in batches, blend soup until smooth.
Transfer soup as blended to a sieve set over a large bowl and force through, discarding seeds. Stir in sugar and salt to taste.
Reheat in cleaned saucepan, if necessary, and serve garnished with avocado, tortilla strips, chopped onion, beans, corn, and/or cilantro.