Cook pasta, and reserve 1 cup of pasta water (if using instead of milk), strain. Toss with a little olive oil to prevent it from sticking together and set aside.
Steam butternut squash until tender, about 10-15 minutes. Set aside.
Heat butter in a large sauté pan over medium heat. Add onions and sauté until translucent, about 2 minutes, and then add garlic, thyme leaves, salt and crushed red pepper. Sauté until fragrant, about 2 minutes more. Then add the butternut squash, mixing well and cooking another 2-3 minutes so all the flavors coat the squash. Add to the blender.
Add ½ cup milk or reserved pasta water and ½ teaspoon salt to the blender. Purée mixture until smooth. Add the remaining milk or pasta water a little at a time until the sauce is silky and will coat the pasta without being too thick and gloppy or too thin and watery. Taste and adjust seasoning as needed.
In the large sauté pan where you cooked the onions (no need to extra dishes!), add the butternut squash purée and cook on medium heat until it is warm. Add the pasta and parmesan cheese and heat a few minutes. Add more milk or pasta water if needed.
Serve pasta topped with extra Parmesan cheese and thyme.