Preheat the oven to 350°F (175°C).
Melt the butter in a large skillet over medium-high heat.
Add the onion, celery, green onion (white parts), and garlic. Cook, stirring frequently, until the vegetables are softened, about 5 minutes.
In a small bowl, whisk the egg yolks and evaporated milk together until well blended. Set aside.
Add the flour to the skillet and stir well into the vegetables to form a roux, cooking for about 2 minutes without letting the flour brown.
Gradually whisk in the milk mixture, stirring constantly to combine.
Stir in the lemon juice, hot sauce, salt, cayenne, and black pepper. Cook for another 4-5 minutes until thickened. If the sauce is too thick, add a little water or milk to reach the desired consistency (similar to thick creamed soup).
Remove from heat and fold in half of the grated cheeses, stirring until melted and fully incorporated.
Divide the crab meat evenly into four mini oven-proof casseroles or a large cast iron skillet (8″x8″ baking dish works too), being careful not to break up the crab lumps.
Pour the cheese sauce over the crab meat and sprinkle the remaining grated cheese on top.
Bake in the preheated oven for 15 minutes until bubbly. Switch the oven to broil and broil for about 5 minutes until the cheese starts to brown (watch closely to avoid burning).
Remove from the oven, garnish with the remaining green onions, and serve immediately.