1. Preheat oven to 375°F (190°C).

2. Bring a large pot of salted water to a boil. Add green beans and blanch for 3–4 minutes, then drain and rinse with cold water.

3. In a large skillet, heat butter and olive oil over medium heat. Add onions and cook until softened and lightly golden.

4. Add mushrooms and sauté until they release moisture and begin to brown.

5. Stir in garlic and cook for 1 minute.

6. Sprinkle flour over the mixture and stir for 1 minute to cook off the raw taste.

7. Gradually add chicken broth, stirring constantly, followed by heavy cream.

8. Simmer for 3–4 minutes until thickened, then stir in Parmesan cheese, salt, and pepper.

9. Add the green beans to the skillet and toss to coat evenly.

10. Transfer mixture to a casserole dish, top with fried onions, and bake for 20–25 minutes until bubbly and golden.