Preheat oven to 350°F.
Heat a large skillet over medium-high heat with 1 turn of the pan of EVOO and 4 tablespoons of butter. Once hot, add the mushrooms and cook, stirring every now and then until brown, about 5 minutes. Add the shallots, garlic, thyme, salt and pepper. Continue to cook until the shallots start to get tender, about 4-5 minutes.
While the mushrooms and shallots cook, place the green beans in another skillet. Add an inch or two of water, salt it and bring to a boil. Cook the beans for 2-3 minutes, drain and shock in ice water.