Make the base: In a large stockpot, combine the celery, parsnips, carrots, onion, 4 cups of the corn, the thyme, hominy, and enough stock and/or water to cover the mixture by 1 inch. Cover and bring to a boil over high heat. Reduce the heat to a simmer, remove the cover, and cook for 2 hours, or until the vegetables are completely softened and cooked through.
Meanwhile, preheat the oven to 375°F. Line a rimmed baking sheet with a Silpat or parchment paper.
Peel and cut the sweet potatoes into 1-inch chunks and place them onto the prepared baking sheet. Drizzle the brown butter over them and turn with tongs to coat. Roast for about 40 minutes, until the potatoes are cooked through and you can pierce them easily with the tip of a sharp knife. (This can either be made while the soup base is cooking or up to 2 days before you plan to serve the soup.)
When the base is cooked, use an immersion blender to purée it until completely smooth. Set aside. (If you wish, this can also be done in a food processor, but it’s best to work in batches and very carefully, because the soup will be hot. When you’re done, return the purée to the pot. The soup base can be prepared up to 2 days before you plan to serve the soup.)
Add the maple sugar, salt, pepper, half the sweet potatoes and the remaining corn kernels to the puréed soup, stir well, increase the heat to high, and bring to a boil. Reduce the heat to medium-low, add the milk or cream, stir, cover, and simmer for 10 to 15 minutes. Ladle into bowls and top with the remaining roasted sweet potato chunks.