° Serves 6 to 8
There is something very elegant about egg dishes, which are versatile and can be served for breakfast, brunch, lunch, or dinner. When I was a kid, we ate a gratin of eggs in one form or another at least once a week. The important thing is to cook the hard-cooked eggs the right way. Use organic eggs, and make a hole in the rounder end of each egg with a pushpin, penetrating the air chamber. This will relieve the air pressure when the eggs are placed in boiling water and prevent them from cracking.
Cook the eggs at a low boil to prevent the whites from toughening. As soon as the eggs are cooked, pour out the hot water and shake the pan to crack the shells, which will make the eggs easier to peel. Add cold water and ice to the pan and set aside until the eggs are thoroughly cooled. (This quick method of cooking the eggs releases the sulfur in them and prevents the yolks from having that green color and sulfur smell.) Shell the eggs under cool running water.
Bring a large saucepan of water to a boil. With a pushpin, punch a hole in the rounder end of each egg and lower them into the boiling water. When the water comes back to a boil, reduce the heat so the eggs cook at a gentle boil. After 10 minutes, pour out the water and shake the eggs in the pan to crack their shells. Add cold water and ice to the pan and let the eggs cool.
Drain the eggs and shell them under cool running water, then quarter them lengthwise and arrange them in a 6-cup gratin dish.
Preheat the broiler. Heat the butter and olive oil in a medium saucepan and add the mushrooms. Cook until the moisture is released from the mushrooms and they are sizzling in the butter, about 5 minutes. Sprinkle the flour on top and mix it in. Add the milk, salt, and pepper and bring to a boil, stirring with a whisk until the mixture thickens. Remove from the heat.
Sprinkle the ham, chives, and half the cheese over the eggs. Pour the sauce on top and sprinkle on the rest of the cheese.
Place the dish under the broiler, not too close to the heat source, and broil for about 10 minutes, until the surface is brown and bubbling. Serve.
Note: To prepare the gratin ahead (even the night before), assemble the dish and refrigerate, covered. When ready to serve, preheat the oven to 400 degrees. Bake the gratin for about 30 minutes, until it is brown, bubbling, and hot.