In a large pot of boiling salted water, cook the fettuccine until al dente. Reserve 3/4 cup of the pasta cooking water and drain the fettuccine well.
Add the ricotta and the 1/2 cup of pecorino to the pot along with the reserved pasta cooking water; stir until smooth. Add the fettuccine and the basil, season with salt and pepper and toss. Serve in bowls, passing additional grated pecorino at the table.