In a large saucepan, heat butter over medium heat. Add onion, garlic, celery, and carrot. Cook, stirring occasionally, until vegetables are tender, about 5 minutes.
Sprinkle flour over the top and mix so all ingredients are coated. Cook for 2 minutes, stirring frequently.
Add squash, broth, and half-and-half. Bring to a boil, then reduce to a simmer. Add sage, thyme, paprika, cayenne pepper, black pepper, salt, nutmeg, and ginger. Simmer for 20–30 minutes (this will be about the same amount of time if the squash is uncooked).
Remove from heat and ladle the mixture into a blender (or use an immersion blender). Puree until smooth. Serve with a dollop of sour cream or cream cheese for garnish. Season with salt and pepper to taste.
Notes
Let the bisque cool to room temperature before storing. Transfer to airtight containers and refrigerate for up to 4 days. For longer storage, FREEZE in freezer-safe containers for up to 3 months.To REHEAT, thaw in the refrigerator overnight if frozen, then warm on the stovetop over medium heat, stirring occasionally, until heated through.