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Preheat your oven to 400°F.
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Boil 4 cups of water in a large saucepan. Add green beans and blanch for 1-2 minutes, until vibrant in color. Remove the beans and transfer to a bowl of ice water to stop their cooking. Drain beans and place them in an 8x8 baking dish.
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In a large skillet, heat 1 Tbsp butter over medium-high heat. Add ¼ diced onion and sauté over medium heat until soft, 2-3 minutes. Add the bread crumbs and salt. Continue to sauté 1-2 minutes, or until bread crumbs are fragrant and toasted. Transfer breadcrumbs to a paper towel-lined plate and set aside.
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In the same (now empty) sauté pan, heat 2 Tbsp butter over medium-high heat. Add the onions and sauté 1-2 minutes, until soft. Add the mushrooms and continue to sauté 1-2 minutes, until they begin to soften.
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Reduce the heat to medium-low. Add the flour, thyme, ground mustard, and pepper. Cook, stirring constantly, for 1 minute.
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Add the broth and milk. Bring the mixture to a simmer over medium heat, and simmer 10-12 minutes, until the gravy has thickened.
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Pour the mushroom gravy over the green beans in the baking dish, and mix to coat. Top the beans with the seasoned bread crumbs. Place the dish in the oven and bake 15-20 minutes, until bubbly to the center.