In a medium pot, heat water over medium to low heat to steam the green beans. You want to steam them first to soften them up a bit before sauteing. Place the green beans on a steamer over the water and cover. Steam for 15 minutes or until the beans have started to soften a bit, but not too much.
Once the beans are done steaming, heat a saute pan over medium heat and add the pine nuts. Cook for about 5 minutes, shaking the pan around every few minutes as to not burn the nuts. After 5 minutes, turn the heat up a bit and add the sesame oil. Add the mushroom and green beans and give the pan a good stir so everything is coated in oil. Cover and cook for 5 minutes. Add salt and pepper and re-cover. Cook for 5 more minutes. Serve immediately.
The nuttiness from the pine nuts and sesame oil go really well with the woody flavor of the mushrooms. The green beans will still be a bit crunchy, not soggy, and the mushrooms hold their texture well as you don't salt the pan until the end.