Pre-heat the oven to 350°F.
Melt the butter in a large skillet over medium-high heat.
Add the onion, celery, green onions (white parts), and garlic, and cook, stirring, until the vegetables are softened, about 5 minutes.
While the vegetables cook, vigorously whisk the egg yolks and evaporated milk together in a small bowl until well blended; set aside.
Add the flour to the skillet, and blend well into the vegetables to create a white roux; be sure to not let the flour brown. About 2 minutes.
Using a whisk, add the milk mixture, stirring constantly to blend into the roux mixture.
Stir in the lemon juice, hot sauce, salt, cayenne, and black pepper, and continue to stir for another 4 - 5 minutes. (if sauce seems too thick, add a little water or milk to thin...should be the consistency of thick creamed soup).
Remove from the heat, and fold in half the cheese; blend until it is totally melted and fully incorporated.
Gently divide the crab meat among four mini oven-proof casseroles, or iron serving dishes; trying not to break up the crab lumps. Or, pour into 1 large cast iron skillet, or 8"x8" baking dish.
Pour the cheese sauce over the crab, and then sprinkle with the remaining grated cheese on top.
Bake until bubbly, about 15 minutes, then reset the oven for broil, and broil until the cheese begins to brown, about 5 minutes (keep an eye on this...don't let it burn!!).
Remove from the oven, sprinkle with the green onions (green parts), and serve at once!