Bring a large pot of water to a boil. Salt the water, then add the pasta and cook until al dente.
Meanwhile, heat a medium heavy-bottomed pot over medium heat. Add the EVOO, 1 turn of the pan, and the butter. When the butter melts into the olive oil, add the thyme, then grate the onion directly into the pot with a handheld grater, such as a Microplane. Cook the onion for 2 minutes, then stir in the flour and cook for 2 minutes more. Whisk in the broth, then stir in the butternut squash and heat until warmed through and smooth. Stir in the cream and bring the sauce to a bubble. Stir in the cheeses and season to taste with salt, nutmeg and pepper.
Drain the cooked pasta, return it to the pot it was cooked in and add the sauce. Stir together and serve.