Preheat the oven to 375°F. Spread the hazelnuts in a pie plate and toast for about 7 minutes, until golden. Let cool. Rub off most of the skins and roughly chop.

In a large pot of boiling salted water, cook the pasta until al dente. Drain the pasta, reserving 1 cup of the cooking water.

Meanwhile, in a medium saucepan, melt the butter. Add the onion, garlic, and sage and cook over moderately low heat until the onion is softened, about 7 minutes. Transfer the mixture to a food processor. Add the pumpkin puree and process until smooth. Season with salt and pepper.

Wipe out the pasta pot. Scrape the pumpkin puree into the pot and cook over moderately low heat until hot. Mix in the mascarpone and the ¼ cup of grated cheese. Add the pasta and the reserved cooking water and toss to coat thoroughly and heat through. Season with salt and pepper. Transfer the pasta to bowls, sprinkle the hazelnuts and chives on top, and serve right away, passing additional Parmigiano at the table.