Chop fine some cold boiled ham. Boil the eggs very hard. With a sharp knife cut them in quarters lengthwise. Remove the yolks, and press them through a coarse sieve or strainer; lay the white segments in warm water. Make a white sauce, using the butter; when melted, add the flour, and let cook for a few minutes; then add slowly the milk. Stir constantly, and when a smooth, consistent sauce, season with salt and white pepper.
Moisten the chopped ham with a little of the sauce, and place it on the fire just long enough to become well heated. Stir constantly so the sauce will not brown. Make a smooth, rounded mold of the ham in the center of a hot dish. Pour over it the white sauce. Sprinkle thickly over the top the yolk crumbs; then range evenly around it the white segments of the eggs.