The Gricia sauce is the predecessor of the Amatriciana. This sauce is very famous in Rome, how it was born is still not clear. Some people say that this sauce was born in the roman countrysides, where the farmers brought only pecorino cheese and guanciale (pork cheek) in the period of the transhumance when they were far from their house for a long time because those products were non-perishable, and then preparing the pasta at the moment with only water and flour, then pulling it on their aprons used for their work as shepherds.
For the gnocchi dough:
For the Gricia sauce: