Preheat oven to 375 degrees F. Grease a 13 by 9 by 2-inch glass baking dish with vegetable oil. Place squash cut side up in prepared dish. Pierce each squash half several times with toothpick or skewer. Bake until squash is tender, about 45 minutes.
While the squash is cooking, use a handheld mixer with the chopping attachment to pulse the cookies until roughly chopped. Set aside.
In a large pot, bring the olive oil up to almost smoking. Quickly cook the sage leaves until crisp. Remove and reserve the sage, and saute the sliced onion. When the squash is done cooking, using a large spoon, scrape squash into the pot; discard peel. Add 3 1/2 cups chicken stock and nutmeg and puree until smooth, add additional stock to reach desired consistency. Stir soup over medium heat until heated through. Season to taste with salt and pepper. Ladle soup into bowls. Top with crushed amaretti; garnish with sage leaves.