6 ounces soft, young pecorino cheese, such as Pientino, coarsely grated
4 ounces best-quality salted butter, cut into 8 pieces
Freshly ground pepper
Remove the fava beans from their pods. Bring a large pot of lightly salted water to a bowl.
Add the beans and cook for 2 minutes. Drain, rinse under cold water, and remove the white skins. This may be done the night before or a few hours ahead of time.
Pulse the garlic in a food processor until finely chopped. Add about two-thirds of the peeled fava beans, the salt, basil, and olive oil. Pulse until roughly chopped, not perfectly smooth. Transfer to a large bowl.
Bring a very large pot of generously salted water to a boil.
Cook the tagliatelle according to package instructions until al dente.
When the pasta is ready, use a spider to lift it out of the water and transfer it to the bowl of fava puree, allowing the water drippings from the pasta to fall into it.
Add about ½ cup of the cooking water, remaining whole fava beans, pecorino, and butter to the bowl and toss until the butter has only just melted and all the ingredients are evenly distributed.