Bring a small pot of salted water to a boil.
Cook the fettuccine until just shy of al dente, reserving some of the starchy pasta cooking water.
Drain the pasta and immediately add it to the melted butter, stirring continuously to emulsify the sauce.
Gradually add the grated Parmigiano-Reggiano cheese, continuing to stir until the sauce is creamy and smooth.
If needed, add a splash of the reserved pasta cooking water to loosen the sauce.
Serve the fettuccine alfredo immediately.
