Preheat the oven to 400 degrees. Cut the squash lengthwise, and with a tablespoon, scoop out the seeds. Wrap the squash in foil, put it on a cookie sheet, and place in the oven. Bake 1 1/2 hours or until squash is very tender when pierced with a long, thin knife. Cool the squash, then unwrap it. Scoop the pulp out from the shell with a tablespoon and place in a bowl. Set aside until ready to use. (Makes about 4 cups cooked squash pulp.)

Heat the butter in a medium saucepan over medium heat. Add the shallots and cook, stirring, until translucent, 6 to 7 minutes. Add the squash pulp, season with salt, and stir well. Add the broth and mix energetically with a wooden spoon or a whire whisk. Bring the broth to a boil, then reduce the heat to low and simmer, uncovered, for 30 to 35 minutes. Stir occasionally during cooking.

Puree the soup through a food mill or in a food processor until smooth and return to the pan. Bring the soup back to a very gentle simmer and cook 5 to 6 minutes longer. Turn the heat off under the pan, adjust the seasoning, and let the soup sit for a few minutes.

Ladle the soup into individual bowls. Sprinkle some chives, almonds, and grated parmigiano on each serving and serve hot.