1. Preheat your oven to 375°F (190°C). Grease a 9×13 inch baking dish and set it aside.
2. Bring a large pot of salted water to a boil. Add the green beans and cook for 4-5 minutes until just tender. Drain and set aside.
3. In a large skillet over medium heat, melt the butter. Add the sliced onions and sugar, cooking slowly until caramelized, about 20-25 minutes. Stir occasionally to avoid burning.
4. Sprinkle the flour over the onions and stir to combine. Cook for an additional 1-2 minutes to cook off the raw flour taste.
5. Gradually whisk in the beef broth and heavy cream, bringing the mixture to a simmer. Cook until the sauce thickens, about 5 minutes.
6. Stir in the Gruyère cheese and thyme, allowing the cheese to melt into the sauce. Season with salt and pepper to taste.
7. Combine the green beans with the sauce, mixing gently to coat. Transfer the mixture to the prepared baking dish.
8. Top with crispy fried onions and bake for 15-20 minutes, or until the casserole is bubbly and golden brown on top.

As you prepare this dish, remember that patience is key, especially when caramelizing the onions. Mama Lou always said, “Good things take time,” and her words have guided me through many a kitchen adventure.