Preheat your oven to 400 degrees. Slice the top off a whole head of garlic to expose the tips of the cloves. Set it cut-side up in a small oven-safe dish, drizzle with 2 teaspoons of olive oil, and cover tightly with foil. Roast for 40 to 45 minutes until the cloves are completely soft and golden when you press them. Set aside to cool. Turn the oven down to 375 degrees for the casserole.

While the garlic roasts, blanch the green beans. Bring a large pot of well-salted water to a boil. Add the trimmed beans and cook for 3 minutes exactly. Drain immediately and plunge them into a bowl of ice water. Leave them there for 2 minutes, then drain and pat completely dry. If using frozen beans, skip this step.

Once the garlic is cool enough to handle, squeeze the soft cloves out of their skins into a small bowl. Mash them into a rough paste with a fork.

In a large saucepan, melt the butter over medium heat. Add the flour and whisk constantly for about 1 minute until the mixture smells slightly toasty and looks like a pale paste. This cooks out the raw flour flavor.

Slowly pour in the warmed milk and half-and-half, whisking constantly as you add it to prevent lumps. Keep whisking over medium heat until the sauce thickens enough to coat the back of a spoon, about 5 to 7 minutes. It should be thick but still pourable.

Remove from the heat. Stir in the roasted garlic paste, grated Parmesan, salt, pepper, and nutmeg. Taste the sauce and adjust salt if needed.

Add the blanched green beans to the saucepan and fold them gently into the sauce until evenly coated. Pour everything into a greased 9x13 baking dish and spread it level. At this point you can cover and refrigerate the dish for up to 24 hours if making ahead.

Scatter the crispy onions in an even layer over the top. Bake at 375 degrees for 25 to 30 minutes, until the sauce is bubbling around the edges and the onions are deep golden brown. Let it rest for 5 minutes before serving.