Place 2 quarts water in a pot and bring to a boil. Salt the water and boil the pasta, stirring frequently, until al dente. Set a strainer over a large heatproof measuring cup in the sink and carefully drain the pasta, reserving 2 cups of pasta water.
Place the Pecorino-Romano in a large bowl and add 1 cup pasta water to the cheese while whisking vigorously. Add the toasted pepper, cream and pumpkin and whisk. Toss in the spaghetti to coat. Season with salt and add additional pasta water if the sauce is too thick. Serve immediately, garnishing with additional freshly ground black pepper and freshly grated cheese.