Melt the butter in a 5- to 6-quart Dutch oven over medium heat. Stir in the onion, carrot, parsnip, turnip, parsley or celery root, and celery and cook, stirring occasionally, until the vegetables begin to soften, about 8 minutes. Stir in the cabbage, ginger, thyme, garlic, 3/4 tsp. salt, and 1/4 tsp. pepper and cook, stirring occasionally, until the cabbage begins to soften, about 3 minutes.
Scoop 1/4 cup of coconut cream from the top of the can and set it aside in a small bowl at room temperature. Add the remaining coconut milk, broth, and the squash and pears to the vegetables. Bring the mixture just to a boil over medium heat, stirring to scrape up any browned bits. Reduce the heat to low, cover, and cook at a bare simmer, stirring occasionally, until the squash is very soft, 20 minutes.
Purée with an immersion blender in the Dutch oven or in batches in a regular blender. Pour the soup through a large coarse strainer set over a large glass measure or bowl. If the soup is too thick, add more chicken broth until thinned to your liking. Season to taste with salt and pepper.
If necessary, reheat the soup in a clean pot. Ladle the soup into bowls, drizzle with the reserved coconut cream, and sprinkle with the lightly chopped thyme.