In a large stockpot, heat oil over medium. Once the oil is shimmery, add the carrots, celery, and onions, and cook until vegetables are soft onions are translucent.
Cut persimmons in half from the bottom and scoop out pulp, removing any hard bits. (The flesh should be dark orange and jammy, with a few dark flecks from sugar caramelization.)
Add sweet potato and persimmon to pot and cook 5 more minutes. Pour in 4 cups broth and stir in turmeric and ginger. Bring to a boil, then reduce to a low simmer. Cover and let cook for at least 30 minutes, until sweet potatoes are completely soft.
Working in batches, puree soup in a blender (or use a stick blender), then return to pot. Taste soup and season with salt and pepper to your liking. If your soup is too thick, add additional broth or water to thin it out. Cook for an additional 15 minutes.
Serve with chopped parsley, Mexican crema, or almond slivers on top, if desired, and bread for dipping.