Blanch the green beans in a large pot of boiling salted water for 3-4 minutes until they are bright green and just tender.
Drain and transfer the green beans to a bowl of ice water to stop the cooking process.Drain again and set aside.
In a large skillet, heat the olive oil and butter over medium-low heat. Add the sliced onions and a pinch of salt. Cook slowly, stirring occasionally, until the onions are golden brown and caramelized, about 15-20 minutes.
Add the minced garlic to the skillet with the onions and cook for another 1-2 minutes until fragrant.
Add the blanched green beans to the skillet with the onions and garlic. Increase the heat to medium-high and sauté for 5-7 minutes until the green beans are heated through and slightly browned in spots.
Season with salt and pepper to taste.
Transfer the sautéed green beans and caramelized onions to a serving platter. Sprinkle hazelnuts on top. Serve hot as a side dish.
This recipe pairs well with a variety of main dishes, including roasted chicken, grilled steak, or baked fish. Enjoy!