Heat a nonstick skillet over medium heat and add the sesame oil. When the oil becomes hot, add onion, peppers and ginger. Saute for 2 to 3 minutes. Add mushrooms, green onion and garlic. Once the vegetables are tender, add broccoli and carrots and place a lid over the pan for 2 to 3 minutes to steam the vegetables. Once tender, stir in mirin, soy sauce and cashews.