Steps

1. Preheat the oven to 400 degrees F. Put the shallots (in their skins) on a small baking dish, roast until soft, about 30 minutes. When cool enough to handle, skin and coarsely chop the shallots. Set aside.
2. Bring a medium-large saucepan of water to a boil over high heat. Add kosher salt, to taste. Add the green beans, and cook, uncovered, until crisp-tender and bright green, about 3 minutes. Drain the beans in a colander and rinse with cold water. Transfer the beans to a large bowl.
3. In the same saucepan, heat the oil over medium heat. Add the mushrooms, season with 1 teaspoon salt, cook, stirring occasionally, until browned, about 7 minutes. Add the mushrooms to the beans.
4. Melt the butter in a small saucepan over medium heat. Add the flour and cook, stirring with a wooden spoon, until golden, about 2 minutes. Slowly whisk in the broth, increase the heat to high, and bring to a boil. Add the shallots, 1 teaspoon of the thyme, and remaining 1/2 teaspoon of salt. Reduce the heat to maintain a simmer and cook until thickened, stirring occasionally, about 5 minutes. Pour the sauce over the vegetables and stir to combine evenly.
5. Spray a 2-quart baking dish with vegetable cooking spray. Transfer the vegetable mixture to the pan. Add the remaining 2 teaspoons of thyme to bread crumbs and scatter over the vegetables. Bake uncovered until the sauce bubbles and the crumbs brown, about 20 minutes.