1. Light the grill or heat the broiler. Coat the steak with 1 tablespoon of the oil. Sprinkle the steak with 1/2 teaspoon salt and 1/4 teaspoon pepper. Grill or broil the steak for 5 minutes. Turn the meat and cook to your taste, about 5 minutes longer for medium rare. Transfer the steak to a carving board and leave to rest in a warm spot for 5 minutes.
2. Meanwhile, put the arugula on a platter or on individual plates. Top with the cherry tomatoes and sprinkle with 1/8 teaspoon salt.
3. In a medium glass or stainless-steel bowl, whisk together the mustard, anchovy paste, vinegar, capers, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Add the remaining 5 tablespoons oil slowly, whisking.
4. Slice the steak on the diagonal. Put the slices on top of the arugula and tomatoes and drizzle the vinaigrette over all.
Variation:: Use two quarts of watercress or spinach leaves instead of the arugula.
Wine Recommendation: The great red grape of Italy's Piedmont is the nebbiolo, the basis of Barolo and Barbaresco, two complex, powerful, expensive wines. Purchase instead a Nebbiolo delle Langhe for a more frugal, lighter, but equally delicious experience.