Step 1In the bowl of a food processor or a blender, puree the anchovies, vinegar, lemon juice, garlic, salt and pepper. With the motor running, add the olive oil in a steady stream through the feed tube to create an emulsion. Taste for seasoning and add more salt, pepper or lemon juice if desired. This makes a generous one-half cup dressing; use the dressing or transfer it to an airtight container and refrigerate it for up to 3 days. Bring it to room temperature before serving.
Step 1In a large wide-mouth bowl, combine the arugula, frisee and endive. Sprinkle with one-half teaspoon salt or to taste, and toss gently with your hands to distribute the salt evenly. Drizzle one-half cup of the dressing and sprinkle over one-fourth cup of the Parmigiano-Reggiano, tossing gently with your hands to coat the lettuce leaves with the dressing. Taste for seasoning and add more salt, dressing or lemon juice if desired.
Step 2Pile the salad on a large plate or divide it among 4 individual plates. Sprinkle the remaining 3 tablespoons of the Parmigiano-Reggiano over the top and serve.