Bring a large pot of water to a boil with 1 tablespoon of salt. Add the green beans and cook for about 5 minutes until bright green and just tender. Transfer them into ice water immediately to stop the cooking.

Toss the sliced onion rings with all-purpose flour and salt. Heat vegetable oil in a skillet over medium heat and fry the onion rings in small batches until golden and crispy, about 3 to 4 minutes per batch. Drain on paper towels.

In a skillet, melt butter over medium heat. Add the finely diced onion and minced garlic, cooking for 2 minutes until softened. Add mushrooms, salt, and pepper. Cook for about 8 minutes until the mushrooms are soft and golden.

Sprinkle in the flour and stir well to coat the vegetables. Cook for 1 minute, then slowly stir in the chicken or vegetable broth. Add heavy cream and continue stirring until the sauce thickens to a creamy consistency, about 4 to 5 minutes.

Preheat oven to 375°F. Combine blanched green beans with the mushroom sauce in a large baking dish. Top with three-fourths of the crispy onions. Bake uncovered for 15 minutes until bubbling.

Remove the casserole from the oven, sprinkle the remaining crispy onions on top, and return to the oven for another 5 minutes. Serve hot.