4 ounces arugula stems discarded and coarsely chopped
Preheat oven to 450. Halve squash lengthwise and seed, cut crosswise into 1 1/2 inch wide slices and season with salt. Roast slices, skin side down in shallow baking pan in middle of oven until tender and golden, about 50 minutes. Set aside 6 crescents shaped squash slices for serving and keep warm. Cut flesh from remaining slices into 1/2 inch pieces, discarding skin.
After squash has been roasting 40 minute, bring broth to a simmer and keep at a bare simmer, covered. Meanwhile, cook onion in butter in a 4 quart pot over moderate heat, stirring until softened, about 6 minutes.
Add rice, garlic and cumin to onions and cook, stirring, 3 minutes. Stir in 1/2 cup simmering broth and cook on medium heat, stirring frequently until broth is absorbed.
Continue simmering adding broth 1/2 cup at a time, stirring constantly and letting each addition be absorbed before adding the next, until rice is creamy looking, but still al dente(it should have the consistency of thick soup), about 18 minutes total. (There will be leftover broth).
Stir in squash pieces, and then stir in cheese, sage and arugula and simmer, stirring for 1 minute.