Preheat the oven to 450°F.
Bring a large pot of salted water to a boil. Clean and trim the beans then place in the boiling water. For small beans, blanch for 2-3 minutes and for larger beans, blanch for 4-5 minutes. Meanwhile, fill a large bowl with ice water. Drain and transfer the beans to the ice water and once cool, drain them and set aside.
In a medium bowl, toss onion rings with flour and a pinch of salt until coated. Place a large, oven-safe skillet on medium-high heat. Add the olive oil and once it is hot, spread the onions evenly in the pan. Fry for 6-7 minutes, tossing often, until lightly browned and crispy. Transfer to a plate and set aside.
Using the same large skillet. Melt butter on medium-high heat. Add the mushrooms, season with a good pinch of salt, and saute for 8-10 minutes, stirring occasionally, until they are deep brown and beginning to crisp.
Sprinkle in the flour and stir until the mushrooms are coated. Cook for 2 minutes, then pour in the chicken stock. Stir until the stock absorbs the flour, then mix in the cream and dijon. Season with fresh pepper, reduce heat, and simmer for 10 minutes, until the sauce is slightly thickened.
While the mushroom cream sauce is thickening, combine breadcrumbs, butter, Parmigiano, and a pinch of salt in a medium bowl. Set aside.
Add the blanched beans to the skillet. Using tongs, carefully toss the beans until all the ingredients are evenly distributed.
Sprinkle the top of the skillet with the breadcrumb topping. Arrange fried onions over top, then place the casserole in the oven to bake for 20 minutes, or until the topping is golden brown.
Allow to cool for a few minutes before serving family style.