Place sweet potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 10 to 15 minutes. Drain potatoes and reserve 2 1/2 cups of potato water. Chop 2 sweet potatoes and Yukon Gold potato when cool enough to handle; reserve remaining sweet potato for a later step.

Heat olive oil in a large pot over medium heat; cook and stir celery and sweet onion in the hot oil until onion begins to brown, about 10 minutes. Stir 1 chopped sweet potato, chopped Yukon Gold potato, and garlic into mixture. Cook and stir until garlic begins to turn golden, about 8 minutes. Stir corn and 1 chopped sweet potato into onion and celery mixture. Cover pot and cook for 5 minutes, stirring occasionally.

Pour reserved 2 1/2 cups drained potato cooking water into mixture. Place remaining sweet potato and ginger into a food processor and pulse several times to chop; puree and stir into vegetables. Stir soy milk, vegetable broth, parsley, rosemary, sea salt, black pepper, and bay leaf into mixture and bring soup to a boil. Reduce heat to low and simmer 5 minutes.

Whisk flour into soup, stir until thickened, and remove soup from heat.