Preheat oven to 375°. Split squash lengthwise and scrape clean. Set cut side up in a 9- by 13-in. baking dish. Score flesh on each half four times in a crisscross (so juices absorb). Sprinkle with 1/2 tsp. salt and spread with honey. Roast until tender when pierced, about 1 1/2 hours, basting occasionally with juices. Let cool.
Meanwhile, in a large pot over medium heat, cook onions and garlic in butter, stirring occasionally, until golden, 20 to 25 minutes. Add sage and carrots; cook, stirring, about 5 minutes more.
Scrape squash from shells into onion mixture and add 1 1/2 qts. broth. Cover and bring to a boil over high heat; reduce heat and simmer until carrots are very tender when pierced, about 30 minutes.
Purée soup a portion at a time in a blender until very smooth. Return to pot and stir in remaining 1 tsp. salt, 1/2 tsp. paprika, the pepper, and nutmeg.
Add corn; heat soup over medium heat, stirring a few times, until corn is tender-crisp, about 5 minutes. Thin with 1 to 2 cups more broth if you like. Ladle into bowls. Top with a spoonful of crème fraîche, a little paprika, and parsley.
Make ahead: Through step 4, up to 1 day, chilled. Reheat before adding corn in step