In a small bowl, whisk 2 Tbs. of the olive oil, the lemon juice, Worcestershire sauce, mustard, and a generous pinch of salt. Season both sides of the steak with 1/2 tsp. salt and 1/4 tsp. pepper.
In a 10-inch straight-sided saute pan, heat the remaining 1 Tbs. oil over medium-high heat until hot. Cook the steak, without disturbing, swirling the oil in the pan occasionally, until the bottom of the steak is deeply browned, about 5 minutes. Flip and cook until the other side is nicely browned, about 3 minutes more. Transfer the steak to a cutting board.
Turn the heat to low and cook the shallots, stirring frequently, until softened and lightly browned, 5 to 8 minutes. (Use a spatula or spoon to break apart the shallot slices and to incorporate some of the browned bits from the pan.) Remove from the heat and let cool slightly.
Slice the beef thinly. Fan an equal number of slices on each of 4 dinner plates. Rewhisk the dressing if necessary. In a large bowl, toss the shallots, watercress, and Stilton with a generous pinch of salt and just enough of the dressing to coat. Season with more salt and pepper and arrange the salad over the beef slices.