Prepare a medium (375°F) gas or charcoal grill fire. Season the steak generously with salt and pepper. Put the tomato slices on a plate, sprinkle with 1/2 tsp. salt, and set aside.
Whisk the vinegar and the mustard in a small bowl. Whisk in the olive oil in a slow stream until emulsified. Stir in the cornichons and shallot and season with 1/4 tsp. each salt and pepper.
Grill the steak until it’s well marked and releases easily from the grates when you lift an edge, 2 to 3 minutes. Flip and grill the other side until medium rare (130°F), 2 to 4 minutes more. Transfer the steak to a cutting board and let rest for at least 5 minutes.
Meanwhile, halve the ciabatta horizontally. Brush the cut sides with oil and sprinkle lightly with salt. Grill cut side down until toasted, about 1 minute. Remove from the grill and line the bottom half with the cheese. Return it to the grill, cheese side up, and cook until the cheese starts to melt and the outside of the bread is toasted, 1 to 2 minutes.
Toss the watercress with half of the dressing in a medium bowl. Thinly slice the steak and season with salt and pepper. Arrange the steak over the cheese, spoon the remaining dressing over the steak, and top with the tomato, watercress, and the top of the bread. Slice and serve.