In a medium skillet over medium-high heat, heat oil and butter and add onion to the pan. Let cook until light brown and caramelized, about 20 minutes.
While the onions are caramelizing cook green beans 5 minutes in 1-inch of boiling water, covered. Drain beans and toss them in the skillet with the finished onions. Season with salt and pepper and toss until combined and hot.