Fill a medium or large pot about three-quarters full with water and bring it to a boil.
While the water heats, trim the top and bottom from the butternut squash. Peel it with a vegetable peeler, cut it in half, and remove the seeds with a spoon. Cut the flesh into roughly 1-inch cubes.
Carefully add 3 cups of cubed squash to the boiling water. Cook uncovered for 12–14 minutes, or until completely tender when pierced with a fork. Drain well.
For easier cleanup, refill the same pot with water and return it to a boil. Add the pasta and cook according to the package directions until just short of al dente. Drain and set aside.
Transfer the cooked squash to a blender. Add the milk, paprika, salt, and black pepper. Blend until completely smooth and creamy.
Pour the butternut squash sauce into the empty pasta pot. Warm it over medium-low to medium heat, stirring occasionally. Avoid bringing the sauce to a hard boil.
Reduce the heat and gradually stir in the freshly shredded cheddar until melted and smooth.
Add the drained pasta and gently stir until every piece is coated in the sauce. If your Butternut Squash Mac and Cheese becomes thicker than you prefer, stir in a small splash of milk until it reaches your desired consistency.
Taste and adjust the salt and pepper if needed. Serve warm.
Notes
Fill a medium or large pot about three-quarters full with water and bring it to a boil.