Make the dressing: place 2 tablespoons olive oil, scallions, cashews, basil leaves, and lemon juice in the bowl of a food processor and pulse until smooth. Season with salt and pepper. Set aside.
Season the chicken with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chicken to the pan and cook until golden brown, about three to four minutes per side. Squeeze half a lemon over the chicken and set aside.
Bring a small pot of salted water to a boil. Add the green beans and cook until crisp, tender, and bright green. Immediately drain the beans and rinse under cold water.
Divide the beans between serving plates and top with chicken, quinoa, and basil. Drizzle cashew dressing and garnish with a lemon wedge.