Heat the vegetable oil over medium high heat in a large skillet.
Place onion slices in a large bowl or resealable plastic bag. Add the flour. Thoroughly coat the onion rings with the flour.
Working in batches, fry the onion rings in the hot oil until they begin to turn golden brown. Remove from pan and drain on a layer of paper towels. Sprinkle with salt.
Preheat oven to 400 degrees.
Steam green beans either in the microwave or on the stovetop in a steamer basket until beans are crisp-tender, about 4-6 minutes.
Melt the butter in a large skillet over medium heat. Add the mushrooms and a pinch of salt. Saute until most of the liquid has evaporated and the mushrooms begin to turn brown. Add the sherry and continue to sauté until most of the liquid has evaporated, about 1 minute. Sprinkle the remaining three tablespoons of flour over the mushrooms and stir to coat.
Slowly whisk in the broth and cream. Reduce heat to a simmer and continue to cook until the liquid begins to thicken, about 10 minutes. Add the green beans to the pan along with salt and pepper. Stir to combine.
Pour the green beans into a prepared 9 x 13 x 2 –inch glass baking dish. Bake for 20 minutes until the sauce around the edge of the casserole begins to bubble. Remove pan from the oven and stir to redistribute the sauce.
Top with fried onions.