SNAP BOTH ENDS OFF THE BEANS and pull off any strings. Cut large pole beans crosswise into 2-inch pieces. Don't cut smaller French haricots verts. Fill a mixing bowl or medium pot with 4 cups cold water and add 1 tray of ice cubes. Set aside. Bring 4 quarts of water with 2 tablespoons kosher salt to a boil over high heat and add the beans. The water will stop boiling when you add the beans. After it has returned to the boil, cook the beans, uncovered, until tender but still crisp. This will take from 3 to 5 minutes depending on the size and age of the beans. Remember that this is only a preliminary preparation so do not overcook the beans. Drain the beans and place them immediately into the ice water. Stir until cool, then drain. Spread the beans on towels and pat dry. Meanwhile, slice mushrooms thinly and set aside on a plate. Heat the oil and butter in a medium skillet over medium heat and add the pine nuts and mushrooms. If using dried tarragon, add it now. Cook, stirring, about 5 minutes. Add the green beans and fresh tarragon and cook until beans are hot, about 3 minutes longer. Transfer to a serving platter and serve immediately.