For the onions:

2 tablespoons butter
2 large yellow onions, thinly sliced lengthwise
salt and ground black pepper to taste
1 tablespoon sherry vinegar

For the white sauce:

2 tablespoons butter
2 ½ tablespoons all-purpose flour
2 ½ cups milk
1 pinch ground nutmeg
1 pinch cayenne pepper to taste
¼ teaspoon ground thyme

For the topping:

2 tablespoons melted butter
⅔ cup panko bread crumbs
2 pounds fresh green beans, trimmed
4 ounces shredded Gruyere cheese, divided
⅓ cup grated Parmesan cheese