Preheat oven to 350°F. Grease a large casserole dish or Dutch oven.
In a large sauté pan over medium high heat, sauté mushrooms in 1 tablespoon of reserved evoo for 5 to 7 minutes, until golden brown and slightly crispy on the edges. Season with salt and pepper, and transfer to a bowl. Set aside.
Add 1 tablespoon more of reserved evoo to the pan, and brown pearl onions for 7 to 10 minutes, or until golden brown. Add garlic to the pan and continue cooking for 1 minute, until the garlic has softened slightly and is very fragrant. Transfer onions and garlic to the bowl with mushrooms.
Add 2 tablespoons more of reserved evoo to the pan and scrape up any brown bits that may be stuck to the pan. Add flour and whisk together with oil. Pour in white wine and cook for 1 minute. Pour in broth, and whisk into a thick sauce. Add mushrooms and pearl onions back to the pan and stir to combine.
Toss green beans with 1 tablespoon of reserved evoo, salt, and pepper. Then fold green beans into the sauce. Pour into prepared casserole or Dutch oven, and bake uncovered at 350°F for 20 minutes. Sprinkle crispy onions on top, and continue baking for 10 minutes more.
Remove from oven and cool slightly before serving.