For soup: Preheat the oven to 350 degrees. Brush the flesh of the squash and pears with olive oil and place, cut side down, on a rimmed baking sheet. Roast until tender when pierced with a fork, about 30 to 35 minutes.
Use a spoon to scrape out the flesh of the squash and pears, and put in the work bowl of a food processor fitted with a metal blade. Discard the skins. Puree until smooth. Add 1 to 2 cups of the chicken broth and continue processing until smooth. Put this mixture in a 3 ½- to 4-quart saucepan, add the remaining chicken broth, cream, nutmeg, and sugar. Bring to a boil, and then reduce to a simmer and cook for 10 minutes. Add salt and pepper to taste.
For croutons: Place the bread cubes in a large mixing bowl. Drizzle the olive oil over, add Parmesan, and toss the bread cubes until thoroughly coated. Spread in an even layer on a rimmed baking sheet and bake until toasty brown, about 10 to 12 minutes. Set aside until ready to serve.
When ready to serve, ladle the soup into a warmed soup tureen or individual soup bowls, garnish with the croutons, and serve immediately.