Preheat the oven to 375 degrees Fahrenheit with a rack in the upper third of the oven.

Grease a medium baking dish with butter.
3. In a medium bowl, whisk together the egg yolks, milk, and heavy cream. Set aside.

In a separate small bowl, combine the bread crumbs and parmesan. Set aside.

In a medium skillet over medium heat, melt 4 tablespoons of butter.

Add the garlic, onion whites and light greens, celery, and bell pepper. Saute, occasionally stirring, until softened and lightly browned in spots, about 5 minutes.

Add the creole seasoning, 1 teaspoon salt (add ¼ teaspoon more if the creole seasoning is salt-free), black pepper, cayenne, and white wine.

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Cook, frequently stirring until the wine nearly evaporates, about 2 minutes.

Reduce to low heat and add the flour. Cook, stirring continuously, until flour is golden brown and smells nutty, about 5 minutes (it won’t darken like a roux). Remove from heat.

Stir in the crabmeat and lemon juice.

Stir in the cream and egg mixture, half of the cheddar, and half of the gruyère until melted (return to low heat if needed to incorporate the cheese fully).

Transfer the crab au gratin mixture to the prepared baking dish and top with the remaining cheddar and gruyère or Swiss cheese.

Sprinkle the dish evenly with the parmesan mixture.

Bake the crab au gratin until bubbly and golden brown on top, 20–30 minutes.

Garnish with the remaining dark green onions, and serve with bread for dipping.