Place the butter in a large heatproof bowl. Using an electric mixer on low speed, beat until smooth. Add whipping cream, and Parmesan cheese. Stir until well blended; set aside.
Bring a large saucepan of lightly salted water to a boil. Add pasta and cook according to package directions. Drain well and immediately add the hot pasta to the butter mixture in the large bowl. Using two forks, toss the fettuccine in the butter mixture to coat well. Add salt and pepper.
Divide the pasta between 4 serving plates. Sprinkle shredded basil over each serving. Serve.