Wash hands with warm, soapy water for 20 seconds.
Cook pasta according to package instructions. Drain and set aside.
If butternut squash is not cooked and puréed, cook it until tender, then purée in a blender or mash with a fork until smooth. If using canned pumpkin, go to the next step.
In a large skillet, electric skillet, or saucepan, melt margarine or butter, or add oil and heat on medium high.
Once heated, add flour. Stir until combined and flour begins to brown, about 2 minutes.
Add butternut squash or pumpkin, broth, garlic, and black pepper. Stir until combined and heated through.
Lower heat to medium. Add milk. Heat, whisking constantly, until combined and warm.
Reduce heat to low. Add cheese and stir until cheese is melted.
Add cooked pasta to the sauce and stir until pasta is completely coated and heated through.