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1
Rinse and drain watercress; pluck off tender sprigs (you should have 1 1/2 to 2 cups). Chop enough of the remaining watercress (including stems) to make 1/4 cup; save leftovers for other uses or discard.
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2
Trim off and discard any mushroom stems to make ends flush with interior of caps; rinse caps and pat dry. In a small bowl, mix olive oil and 1 tablespoon Worcestershire. Rub mixture evenly over smooth sides of mushroom caps. Sprinkle both sides lightly with salt and pepper. Lay caps, gill side down, on a rack in a 10- by 15-inch broiler or baking pan.
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3
Broil about 4 inches from heat until juice starts to drip from mushroom caps, 4 to 5 minutes. Turn caps over and broil until juice in caps bubbles and mushrooms are flexible, 5 to 7 minutes longer.
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4
Meanwhile, combine shallots, vinegar, and tarragon in an 8- to 10-inch frying pan; boil over high heat, stirring often, until all the liquid has evaporated, about 1 minute. In another small bowl, mix cornstarch with 2 tablespoons water until smooth; whisk in milk, mustard, and remaining 1 teaspoon Worcestershire. Add to shallot mixture and stir until boiling. Add salt and pepper to taste.
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5
Transfer mushroom caps to dinner plates. Tuck watercress sprigs alongside caps. Spoon sauce equally over mushrooms and sprinkle with chopped watercress.
