Follow the steps in order for the best result.
In a large skillet, melt the butter over medium heat.
Add the chopped green onions to the melted butter and sauté until they become softened and fragrant.
Incorporate the fresh parsley and flour into the skillet. Stir continuously to ensure the flour dissolves completely and no lumps remain.
Pour in the half-and-half, followed by the grated Swiss cheese. Continue stirring until the cheese is fully melted and the sauce is smooth and creamy.
Gently fold in the crab meat, being careful not to break it apart too much.
Season with kosher salt to your preference. For a touch of heat and visual appeal, garnish with a sprinkle of cayenne pepper.
Serve the Crab Mornay warm in bread bowls, accompanied by melba toast for dipping and enjoying the rich, cheesy sauce.