How to Make It
Put the eggs in a medium saucepan filled with cold water and bring to a rapid boil. Cover and let stand off the heat for 10 minutes. Drain and fill the pan with cold water, shaking the eggs against the side of the pan to crack them. Peel the eggs and coarsely chop them. In a medium bowl, combine the mayonnaise, paprika, dry mustard, chives, Worcestershire and hot sauce. Add the chopped eggs and celery and season with salt and pepper. Refrigerate the egg salad.
Meanwhile, light a grill. Brush the steaks and pita bread with oil. Grill the pita for 30 seconds per side, just until heated and lightly toasted. Immediately wrap in foil to keep soft. Season the steaks with salt and pepper and grill over moderately high heat for about 10 minutes, turning once, for medium-rare meat. Transfer the steaks to a board and let rest for 10 minutes. Thinly slice the steaks across the grain.
In a medium bowl, whisk the lemon juice with the 2 tablespoons of olive oil. Add the watercress, season with salt and pepper and toss. Spread the egg salad over the pita breads (don't slice them open). Arrange the sliced steak on one half of the pita and top with the watercress. Fold the pitas to close and serve the sandwiches right away.