1. Season the chicken with salt and pepper. In a skillet heat the oil, add the chicken pieces, skin side down, and cook until brown. Turn the pieces, partly cover the skillet and cook until the chicken is tender, about 30 minutes.
2. Preheat the oven to 350 degrees F.
3. In a saucepan, melt the butter, add the flour and stir with a wire whisk until blended. Bring the half and half to a boil and add all at once to the butter-flour mixture, stirring vigorously with the whisk until the sauce is thickened and smooth. Stir in 1 tablespoon of the cheese. When it has melted, stir in the egg yolks lightly beaten with a little of the hot sauce.
4. Sprinkle the bottom of a flat casserole with 1/4 cup of the cheese, arrange the chicken on the cheese and spoon the sauce over the top. Place the casserole in the oven and bake 5 minutes, or until thoroughly heated.
5. Combine the remaining cheese with the crumbs, sprinkle over the chicken and broil until golden brown.