Cook the pasta according to package directions. Drain. Reserve one cup of the pasta water.
Reheat the reserved pasta water and bring to the boil.
Add the mussels to the boiling water. Pour in the white wine. Boil until the mussels open, about 2 to 3 minutes.
Scoop out the mussels and allow the liquid to continue boiling until reduced to half. You want a more concentrated mussel stock with the full bodied flavor of the wine so reduce, reduce, reduce.
Meanwhile, open the mussel shells and discard the empty halves.
To the reduced liquid in the pan, add the crumbled cheeses. Stir until melted.
Turn off the heat. Season lightly with salt and generously with pepper.