Melt the butter in a heavy-duty 4- to 5-quart pot over medium heat. Add the onion and cook, stirring occasionally, until tender, 6 to 8 minutes. Stir in the pumpkin and garlic and cook, stirring, 1 minute more. Add the wine and the sage leaves and cook, stirring, until the wine evaporates, about 5 minutes. Stir in 4 cups of broth, cover, and simmer, adjusting the heat as needed, until the pumpkin is very tender, about 25 minutes.
Add 1/4 cup of the Gruyère and using a handheld or standard blender, purée the soup (in batches, if necessary). Season to taste with salt and pepper.
Return to a gentle simmer, stirring constantly and adding more broth as necessary to achieve a thin soup with the consistency of heavy cream.
Position a rack about 6 inches from the broiler and heat the broiler on high. Arrange the bread on a baking sheet. Toast under the broiler, 1 to 2 minutes per side. Sprinkle the croutons with the remaining 2 cups cheese and the minced sage and season with pepper. Broil until the cheese melts and is bubbly, about 2 minutes. Ladle the soup into warm bowls and serve with the croutons.
The soup can be made (without the croutons) up to 3 days ahead. Cool, cover, and refrigerate. Reheat to serve.