Heat the oven to 375°F and position a rack in the center. Lightly grease a 2-quart baking dish.
Bring a large pot of well-salted water to a boil. Add the green beans and cook 3 to 4 minutes until bright green and crisp-tender. Drain, plunge into ice water to stop the cooking, then drain again and pat very dry so the sauce clings well.
In a medium saucepan over medium-low heat, whisk together the condensed mushroom soup, milk, soy sauce, Worcestershire, black pepper, garlic powder, and paprika. Warm until smooth and steaming, 3 to 4 minutes. Stir in 1/2 cup of the cheddar just until melted; remove from heat.
Combine the blanched beans with the warm sauce in a large bowl. Fold in 1/2 cup of the crispy fried onions. Transfer to the prepared baking dish and sprinkle the remaining 1/4 cup cheddar evenly over the surface.
Cover the dish tightly with foil and bake for 15 minutes.
Uncover, stir gently to redistribute the sauce, then scatter the remaining 3/4 cup crispy fried onions over the top. Bake 8 to 10 minutes more until bubbling and the onions are golden. For an extra-crisp finish, broil for 30 to 60 seconds, watching closely.
Let the casserole rest 5 minutes before serving to set the sauce.