Bring a pot of water to a boil for the pasta. Salt the water then add the pasta and cook to al dente.
While the pasta cooks, heat a medium-size, heavy-bottomed pot over medium heat. Add the EVOO, 1 turn of the pan, and butter. When the butter melts into the oil, add the thyme and grate the onion directly into the pot with a hand-held grater or microplane. Cook the grated onion 1-2 minutes, then add flour and cook together 1-2 more minutes. Whisk in stock, then combine with butternut squash until warmed through and smooth. Stir in cream or half-and-half and bring sauce to a bubble. Stir in cheeses in a figure-8 motion and season the completed sauce with salt, nutmeg and pepper. Taste to adjust seasonings.
Drain cooked pasta well and combine with sauce.