Cook pasta as indicated on package directions. (For chickpea pasta, I recommend cooking for 1-2 minutes less than the package suggests.)
Strain cooked pasta and rinse with cool water to stop cooking. If desired, drizzle with oil and toss to prevent clumping.
Over medium-high heat, combine milk, butter, cheese, salt, and pepper in saucepan. Cook over low heat until melted and integrated, stirring continuously.