Lightly coat the squash halves with 1 teaspoon of the vegetable oil. Season the inside with salt and pepper and place cut-side down on a baking sheet lined with parchment paper. Bake until very tender, about 45 minutes. When the squash is cool enough to handle, scoop out the flesh and reserve. Discard the peel.
In a large saucepan over medium-high heat, add the remaining vegetable oil and, when hot but not smoking, add the sausage. Cook until golden brown, about 4 minutes. Add the onions and cook, stirring, until the onions wilted and starting to caramelize, about 6 minutes. Add the garlic, sage and marjoram, and cook, stirring, for 1 minute. Add the cooked squash and chicken stock, stir well to combine, and bring to a boil. Reduce the heat to low, and simmer for 30 minutes, stirring occasionally.
With a hand-held immersion blender, or in batches in a food processor or blender, puree the soup. Strain through a fine mesh strainer into a clean saucepan. Add the cider vinegar and stir to combine. Add the cream and adjust seasoning, to taste.
In a small saute pan, cook the butter over medium-high heat until it begins to turn brown around the edges. Add the whole sage leaves and cook until crisp, 1 to 2 minutes. Transfer the leaves to paper towels to drain.
Serve the soup in bowls, garnished with the crispy sage leaves.