Finely chop the onion and celery ribs.

Sauté the chopped onions and celery in butter in a large skillet over medium heat until softened.

Add flour to the skillet and blend with the butter and vegetables, creating a roux.

Slowly add milk to the roux, blending continuously to avoid lumps.

Remove the skillet from the heat.

In a separate bowl, whisk the egg yolks lightly.

Temper the egg yolks by slowly adding a small amount of the hot milk mixture to the yolks, whisking constantly.

Pour the tempered egg yolk mixture back into the skillet with the milk and roux.

Add the fresh crabmeat, salt, pepper, and grated Cheddar cheese to the skillet.

Gently stir all ingredients together until well combined.

Pour the crabmeat mixture into a casserole dish.

Sprinkle additional Cheddar cheese on top of the casserole.

Bake in a preheated oven at 375°F (190°C) for 35-40 minutes, or until golden brown and bubbly.

Let cool slightly before serving.