How to Make It
Put the eggs in a medium saucepan and cover with hot tap water. Bring to a boil over high heat, then lower the heat to moderate and simmer for 10 minutes. Drain off the water and shake the pan to lightly crack the eggs. Add ice and cold water to the pan and let stand until the eggs are cold. Drain and peel the eggs.
Meanwhile, in a medium skillet, melt 1 tablespoon of the butter over moderately high heat. When the foam subsides, ad the scallions and cook until just wilted. Add the mushrooms and cook, stirring occasionally, until all the liquid is evaporated and the mushrooms begin to brown, about 10 minutes. Stir in the anchovy and season with salt and pepper. Spread the mushroom mixture on the bottom of a 6-cup gratin dish. Slice the eggs with an egg slicer, arrange them over the mushrooms in an even layer and season lightly with salt and pepper.
Preheat the broiler. Wipe out the skillet and melt 1 teaspoon of the butter. Add the onions and 1/2 cup of water and cook over moderately low heat until they are tender and the water is almost evaporated, about 12 minutes. Transfer the onions to a food processor and puree.
In a medium saucepan, melt the remaining butter. Whisk in the flour until blended and cook for 15 seconds. Add the milk and bring to a boil, whisking frequently. When the sauce thickens, add the cream and the onion puree, season with salt and pepper and bring to a boil. Pour the sauce over the eggs, shaking the dish gently to let the sauce seep down. Sprinkle the cheese on top and broil for 3 to 4 minutes, until browned and bubbling.
Hardcooking eggs properly is a simple yet delicate process. Very often, the eggs served in restaurants or cafeterias have rubbery whites and green-tinged yolks and a strong sulfur smellall clear signs that the eggs were cooked for too long a time over too high a heat.
For perfect hard&3150;cooked eggs, begin by piercing raw eggs at their rounded ends, where they is an air space, using either a little device designed for the purpose, or a push pin; this will make it easier to peel the eggs once they are cooked. Then gently lower the eggs into a pan of hot tap water and bring to a light boil; for large eggs, count 10 minutes from the time the water boils, keeping the water at a gentle boil at all times.
As soon as the eggs are done, pour off the water and shake the pan to crack the egg shells. Immediately add ice and cold water to the pan and let the eggs stand until they are cold. At this point the eggs can be shelled.