Wash hands with soap and water for 20 seconds.
Bring a large pot of water to a boil.
Scrub the squash with a clean vegetable brush under running water. Peel, seed, and dice the squash; set aside.
Heat oil in a separate sauté pan, add the sage leaves (if using) and sauté for 1-2 minutes until crispy. Transfer the sage leaves to a separate plate; set aside.
Add garlic to the pan and sauté for 1 minute, stirring occasionally. Then add the butternut squash and stock; stir to combine. Continue cooking until the stock reaches a simmer. Reduce the heat to medium-low, cover, and cook for 10 minutes, stirring occasionally, until squash is tender and mashes easily with a fork.
Transfer squash mixture to a blender. Add in milk and stir the mixture. Then very carefully pulse the mixture until smooth, releasing air pressure as needed.
Add pasta to boiling water and cook according to package instructions until al dente. Reserve 1 cup of starchy pasta water for later. Drain the pasta.
Return butternut squash mixture back to sauté pan over medium-high heat. Add in cheese, and stir until it has melted into the sauce.
Taste and season sauce with salt and pepper as needed.
Once pasta is drained, return it to the stockpot. Pour the butternut cheese sauce on top of the pasta, and toss to combine. If the sauce is too thick, add in some of the hot starchy pasta water to thin it out.
Serve warm, and garnish with crispy sage leaves if desired.