In a medium to large nonreactive bowl, combine the minced shallot, 1/4 teaspoon salt, and the vinegar. Let stand, stirring once, for 15 minutes.
Preheat a grill to medium-high heat. Lightly oil the grate with the 2 teaspoons olive oil.
Season the steak with 1/2 teaspoon salt and a few grinds of pepper. Grill the steak 4 to 6 minutes per side, depending on thickness and heat, for medium rare. Transfer the steak to a plate, cover loosely with foil, and let rest in a warm area.
Meanwhile, to the shallot mixture add the remaining 2 tablespoons olive oil, mustard, and Worcestershire sauce. Whisk the vinaigrette to emulsify. Whisk in 1 tablespoon of the juices from the resting steak and season to taste with salt and pepper.
Arrange the arugula on a serving platter. Top with the grapes.
Slice the steak against the grain into ¼-inch slices and arrange the slices atop the arugula. Whisk any remaining steak juices into the vinaigrette and drizzle over the steak and salad.
Sprinkle with the Parmesan and season to taste with salt and pepper, if desired. Serve immediately.