Prep the oven and pan: Heat oven to 375°F (190°C). Grease a 9x13-inch baking dish or similar casserole dish.
Blanch the green beans: Bring a large pot of salted water to a boil. Add green beans and cook 3–4 minutes until bright green and slightly tender.
Drain and rinse under cold water to stop cooking. Pat dry.
Sauté the mushrooms: In a large skillet, warm butter and olive oil over medium heat. Add mushrooms and a pinch of salt.
Cook, stirring occasionally, until browned and most liquid evaporates, about 6–8 minutes. Add garlic and cook 30 seconds.
Make the sauce: Sprinkle flour over the mushrooms and stir for 1 minute to cook off the raw taste. Slowly whisk in broth, scraping up any browned bits.
Add milk or half-and-half and bring to a gentle simmer. Cook 2–3 minutes until thick and silky.
Season well: Stir in soy sauce or Worcestershire, pepper, and salt to taste. Add a pinch of nutmeg or thyme if using.
If you like, melt in the Parmesan for extra savoriness.
Combine: Fold the blanched green beans into the sauce. The mixture should be creamy but not soupy. Adjust seasoning as needed.
Assemble: Transfer to the prepared baking dish.
Top evenly with half of the crispy onions.
Bake: Bake uncovered for 15 minutes, until bubbling around the edges.
Finish with crunch: Sprinkle the remaining crispy onions on top. Bake another 5–8 minutes until the topping is deeply golden.
Rest and serve: Let sit 5–10 minutes before serving so the sauce sets slightly. Serve warm.