Cut the top 1/4 off 8 squashes, reserving the lids. Scrape the seeds out, clean, rinse, and pat dry. Toss the seeds with 3 tablespoons oil and salt, and arrange in one layer on a baking sheet. Bake in the middle of the oven, stirring occasionally, for 1 hour to 1 1/4 hours, or until they are golden and crisp.
Increase the oven heat to 350 degrees F.
Bake the squashes and the lids, cut side down on lightly oiled baking sheets for 40 minutes or until they are tender (the lids will probably be ready at 30 minutes). When cool enough to handle, scrape most of the pulp out of the squashes leaving just enough in each squash so that it retains its shape. Reserve all the pulp.
Cook the onion in the butter in a skillet, over low heat for 5 minutes or until it is softened. Add the pumpkin pulp and the chicken stock and simmer the mixture for 20 minutes.
Puree the mixture in batches in a blender and transfer to a saucepan.
Heat 2 inches vegetable oil to 350 degrees F. in a deep saucepan. Add the sage in small batches (it will bubble up) and fry for 20 seconds or until translucent. Transfer to paper towels to drain and sprinkle with salt.
Warm the squash shells and lids in a 350 degree F. oven for 15 minutes. Heat soup until hot, adding water if necessary to thin it slightly. Add salt and pepper, to taste. Put each of the shells into shallow soup bowls and ladle some of the soup into the shell. Top with a few fried sage leaves and some Parmigiano-Reggiano shavings and place the lid, slightly askew, on top.