While the hot-water tap runs, put the peas in a 1 1/2 quart microwave-safe container. Add 3 tablespoons hot tap water, cover and cook in a microwave oven on high power for 7 minutes.
Meanwhile, melt 1 1/2 tablespoons of the butter in a large, heavy skillet over medium-high heat. Remove and discard any stems from the mushrooms and thinly slice the caps. Remove the tough, small strip on the sides of the scallops. If necessary, cut the scallops to make them as close to uniform in size as possible.
Raise the heat under the skillet to high and add the scallops. Cook for 1 1/2 minutes, turning once halfway through. Add the mushrooms and cook for 2 minutes. Add the herbes de Provence, vermouth and salt and pepper to taste. Cook for 3 minutes while you coarsely chop the chives. The mushrooms will be just wilted and the scallops lightly browned.
Put the cooked peas and their liquid in a food processor with the remaining 1 1/2 tablespoons of butter and salt and pepper to taste, and puree. To serve, ring a serving platter with the puree and put the scallops and mushrooms in the middle. Sprinkle with the chives.
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