The kabocha squash-bumpy, squat, and unseasonably green has a deeply flavored meat and a more fiery orange than that of its famous cousin. The soup can be made 3 days ahead and chilled, covered.
Roast squash:
Preheat oven to 400 F. Roast squash, cut sides down, in an oiled roasting pan in oven until tender, about 1 hour. Cool and scrape flesh from skin.
Fry sage leaves while squash roasts:
Heat vegetable oil in a deep small saucepan until it registers 365 F on a deep fat thermometer. Fry sage leaves in 3 batches until crisp, 3 to 5 seconds. Transfer leaves with a slotted spoon to paper towels to drain.
Cook pancetta and make soup:
Cook pancetta in a 4 quart heavy pot over moderate heat, stirring, until browned. Transfer pancetta with slotted spoon to paper towels to drain.
Add olive oil to pancetta fat remaining in pot, then cook onion, stirring, until softened. Stir in garlic and chopped sage and cook, stirring, until fragrant, about 1 minute.
Add squash, broth, and water and simmer 20 minutes to blend flavors. Purée soup in a blender, transferring to a bowl.
Return soup to pot and reheat. If necessary, thin to desired consistency with water.
Stir in vinegar and salt and pepper to taste. Serve sprinkled with pancetta and fried sage leaves.
