Bring a large pot of salted water to a boil. Add the fresh green beans, trimmed and halved, and blanch them for about 3-4 minutes until they’re bright green and just tender. Drain immediately and rinse under cold water to stop the cooking process. Set aside.
In a large skillet, melt the unsalted butter over medium heat. Add the diced onion and sauté for 3-4 minutes until translucent and fragrant. Add the minced garlic and cook for another 30 seconds, stirring constantly.
Sprinkle the all-purpose flour over the onions and garlic, stirring well to form a roux. Cook for about 1-2 minutes to remove the raw flour taste.
Slowly whisk in the milk and chicken broth, ensuring there are no lumps. Continue whisking and cooking until the mixture thickens, about 5 minutes.
Stir in the paprika, ground black pepper, and salt to taste. Gradually add the grated sharp cheddar and Parmesan cheese, stirring until the cheese has fully melted and the sauce is creamy and smooth.
Add the blanched green beans to the cheese sauce, stirring gently to coat the beans evenly.
Transfer the cheesy green beans mixture into your baking dish, spreading it out evenly.
Sprinkle the French fried onions generously over the top of the casserole. This will give the dish a crunchy, golden crust once baked.
Preheat your oven to 350°F (175°C). Bake the casserole uncovered for 20-25 minutes, or until the topping is golden brown and the casserole is bubbling.
Let the casserole cool slightly before serving. This dish pairs wonderfully with roasted meats or can be enjoyed as a hearty vegetarian side.