Preheat your oven to 475F. In a large mixing bowl, combine the onions, ¼-cup flour, panko and salt and toss to combine. Grease a sheet pan with 1 tablespoon of olive oil and evenly distribute the onion mixture. Bake the onions in the middle of the oven until golden brown, tossing and turning the onions once or twice while they cook, about 30 minutes. Remove from the oven, set aside, and turn the oven down to 375F.
Bring a pot of salted water to a boil. Add the green beans and cook for about 5 minutes, just until al dente. Drain the cooking liquid and add cold water and a few pieces of ice to arrest the cooking. When very cool, drain again and set aside.
In a medium-sized fry pan over medium high heat, melt the butter and 1 tablespoon of olive oil. Add the mushrooms, season with salt and pepper, and cook until water from the mushrooms has evaporated. To the mushrooms, sprinkle 2 tablespoons of flour and cook, stirring constantly until some of the raw flour flavor has cooked off. Add the half-and-half in slowly, mixing constantly to avoid developing lumps of flour. Bring the mixture to a simmer, taste, and season with salt and pepper. Cook until the mixture thickens, about five minutes.
Off heat, stir in the ravioli and the green beans. Pour the mushroom-ravioli mixture into the prepared casserole dish. Top with crispy onions and bake until heated through and golden brown, about 15 to 20 minutes. Serve hot.