To make the vinaigrette: In a small bowl, whisk together the olive oil, vinegar, and shallot. Season with salt and pepper to taste. Let stand for 30 minutes to allow the shallot flavor to mellow. Taste and adjust the balance as needed.

Blanch the fava beans in a large pot of boiling water until tender (remove one, peel, and taste to be sure), 2 to 3 minutes. Drain and transfer to ice water to stop the cooking. Drain again. Remove outer skin, which should slip off easily.

Remove the outer green leaves from each head of butter lettuce until you reach the pale green heart. (Save the outer leaves for sandwiches or other uses.) Wash the hearts, tear the leaves into smaller pieces, and dry thoroughly.

In a medium bowl, toss the butter lettuce and 1 tablespoon of the parsley with all but 2 teaspoons of the dressing. Season with salt and pepper to taste. Divide leaves among 4 salad plates or arrange on a large platter. With a cheese plane, shave the pecorino into thin shards. Break up the shards by hand if large and scatter over the lettuce. Toss the fava beans with the remaining 2 teaspoons of dressing; season with salt and pepper to taste. Scatter the fava beans over the salad, then garnish with the remaining 1 tablespoon of parsley. Serve immediately.