Preheat a grill to medium-high (about 450°). Generously salt steaks on both sides.
Thread mushrooms onto 4 (8-in.) skewers and brush with oil. Grill mushrooms, turning occasionally, until well browned and cooked through, about 15 minutes.
Meanwhile, finely chop shallots. Heat 2 tbsp. oil in a large cast-iron skillet on grill. Add shallots and cook, stirring often, until tender, 3 to 4 minutes. Add sherry; cook until reduced by half, about 2 minutes. Stir in broth, mustard, Worcestershire, cream, and salt and pepper to taste. Simmer until slightly reduced and beginning to thicken, 3 to 4 minutes. Add butter and cook, stirring, until butter melts. Remove skillet from grill and cover to keep warm.
Season steaks with pepper and grill about 2 minutes per side for medium-rare. Let rest 5 to 10 minutes on a platter. Push mushrooms off skewers and cut in half or thickly slice.
Arrange steaks on plates. Drizzle with a bit of juice from the platter if you like, then the shallot sauce. Top with mushrooms and chives. Arrange some dressed watercress next to each steak.