Put a pot of salty water on the stove to boil and have a bowl of ice-filled water ready on the side. When the water is boiling, put in the beans and parboil for 2 minutes. Remove beans with a slotted spoon and dunk them in the ice water to stop them from cooking further. When they have cooled, drain and set aside.
Heat 1 to 2 tablespoons vegetable oil in a large sauté pan over medium-high heat. Add the sliced mushrooms and sauté until they begin to brown, about 5 minutes. Add the parboiled green beans and continue to sauté until they, too, are slightly browned, another 5 minutes. Turn off the heat and immediately add the soy sauce. Toss the ingredients to coat. When they have cooled a minute, add the sesame oil, toss again and serve.