Preheat oven to 400 degrees F.
Heat a large oven-safe skillet oven low heat and add olive oil, onions and 1/4 teaspoon salt. Stir well to coat, then cover and cook onions until caramely, about 20 minutes, stirring occasionally. While onions are caramelizing, boil a large pot of water. Once boiling, add green beans and cook for 5 minutes, then drain and run cold water over top, letting sit in the sink to air dry and until you’re ready to use.
In a separate small bowl, combine panko with thyme and oregano. Set aside.
Once onions are caramelized, remove with kitchen tongs and set aside in a bowl. Add butter to skillet, then add chopped mushrooms and toss well to coat. Cook for 6-8 minutes until juicy and and soft, then add in half of the onions and the garlic and cook for 30 seconds. Increase heat to medium-high and sprinkle flour over top. Stir well to coat and distribute, cooking for 2-3 minutes. Pour in chicken stock and half and half. Stirring constantly, let mixture come to a bubble, then let cook for 2-3 minutes until just slightly thickened. You don’t want it TOO thick since it will also cook in the oven. Season with remaining salt, pepper, nutmeg and then stir in 1 tablespoon of parmigiano reggiano. Add green beans and toss well to coat.
Cover the top with remaining caramelized onions, seasoned panko and the remaining tablespoon of cheese. Bake for 25 minutes, or until mixture is bubbly and bread crumbs are golden. Serve immediately!