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Trim the beans and cut them into half diagonally. Preheat oven to 350 deg. F.
Bring a pot of salted water to the boil. Add the green beans and boil for another 5 minutes. Drain the beans and immediately plunge them into ice water to retain the crunchiness. Drain again and set aside. in a 9 by 13-inch baking dish.
In a large saucepan, heat enough oil for deep frying the onions. Combine the flour and paprika in a bowl. Season with salt and pepper. Roll the shallots lightly in the flour mixture so that they get coated evenly. Tap off the excess flour and place half of the shallots in the hot oil. Fry until golden and crispy. Remove and drain on paper towels. Repeat the same for the remaining shallots. Once all the shallots have been fried, season them with salt and pepper.
Melt the butter in a large skillet over a moderate heat. Add the sliced mushrooms and cook without stirring until browned. Pour in the mushroom soup, milk, water, lemon juice, soy sauce, and tarragon and mix well. Bring the sauce to a simmer and take off fire.
Place the green beans in a deep baking dish. Pour in the sauce over the beans and stir. Add half the shallots and stir again. Bake for 30 minutes or until the sauce begins to bubble. Place the remaining shallots on top and bake for another 5 minutes. Serve immediately.