Peel and cube the butternut squash or buy squash already cut and peeled.
Place the cubed squash on a large cookie sheet and sprinkle with olive oil.
Bake at 400° for 40 minutes. Turn the pieces of squash every 10 minutes.
Grate the cheese. You can use cheddar or a combination of sharp, white and cheddar.
Get a large pot of salted water boiling. Put the pasta in the pan and cook for 16 minutes.
Once the squash is done, place the hot squash in a food processor or a blender. Put the butter in with the squash and start pulsing. After 5 pulses, turn the machine on and pour the milk into the squash through the spout in the lid.
Once the squash mixture is smooth, pour into a large skillet and bring to a gentle boil on medium low.
Add the cheese and stir until it is melted. If the sauce is too thick, add 1/2 cup of pasta water and stir until blended.
When the pasta is done, drain it and pour into the squash and cheese mixture. Use more pasta water if the sauce is too thick.