Heat oven to 375°F (190°C). Bring a large pot of unsalted water to a boil. Add trimmed cut beans and cook 4–5 minutes until bright green and crisp-tender. Drain thoroughly and spread briefly on a clean towel to remove surface moisture.

Melt butter in a large deep skillet over medium-high heat. Add mushrooms and cook 8–10 minutes, stirring occasionally, until their liquid has evaporated and they begin browning. Add garlic and cook 30 seconds.

Stir in flour and cook 1 minute. Gradually whisk in milk and broth, then add salt and pepper. Bring to a gentle simmer and cook 4–6 minutes, stirring, until sauce coats a spoon.

Fold in drained beans and transfer to a 2.5–3-quart baking dish. Bake uncovered 20–25 minutes until bubbling. Scatter crispy onions over the top and bake 5 minutes more, watching to prevent burning, until the center reaches 165°F.

Let stand 5 minutes before serving. Refrigerate leftovers in shallow containers within 2 hours, or 1 hour above 90°F, at 40°F or below. Use within 3–4 days and reheat to 165°F.