Bring meat to room temperature. Heat a large cast-iron skillet over medium-high heat.
In a large, nonstick skillet, heat 2 tablespoons EVOO, 2 turns of the pan, over medium-high heat. As the oil heats up, slice the potatoes as thin as possible and combine with shallots. Arrange the shallots and potatoes in single layer in the hot skillet and season with salt and pepper. Cook 5-6 minutes, turn and season the flip-side of potatoes and cook 3-4 minutes more. Add watercress to pan, turn and toss with crispy potatoes. Sprinkle a little nutmeg over the hash, to taste.
While the potatoes cook, season steaks with salt and pepper and add to the hot cast-iron skillet. Cook 10 minutes, turning once for rare to medium-rare and up to 16 minutes for medium-well. Remove meat from skillet and let rest 10 minutes before slicing. Meanwhile, reduce heat under skillet a little and add butter to melt. Whisk in flour, cook 1 minute, then whisk in stock, Worcestershire, horseradish and cream. Season with pepper.
Slice steak against the grain. Serve 6 ounces or half of a sliced steak per person topped with the gravy. Serve hash alongside.