Bring a large pot of heavily salted water to a boil.
In a large sauté pan over medium-low heat, warm the heavy cream until hot but not boiling.
Add the Parmigiano Reggiano, Asiago, Fontina, and Gorgonzola a little at a time, stirring continuously until fully melted and smooth.
Season lightly with salt and generously with freshly cracked black pepper. Let the sauce simmer gently for 10–15 minutes, stirring occasionally, until velvety and slightly thickened.
Cook the gnocchi until they float to the surface, about 1–2 minutes.
Transfer the gnocchi directly into the cheese sauce with a ladle of pasta water and toss gently until fully coated.
Serve immediately with extra cracked black pepper.