When the potatoes are cooked, drain and immediately add the anchovies and butter. Mash into a smooth puree. Add the milk and cream.

Now grate the cheese and chop the parsley. Beat the eggs very well in a separate bowl.

When the potato mixture has cooled enough so as not to cook the beaten eggs, add them as well as the grated cheese, parsley, and black pepper. Salt if necessary. The mixture will be smooth, having the consistency of batter.

Place a heavy, well-cured 9-inch skillet on the stove. Pour in the olive oil. Turn on the heat to medium. When the oil is nearly smoking, place the egg mixture in the pan. Be sure it is distributed evenly. Turn down the heat to very low and cook the frocia slowly for about half an hour until it is a rich golden brown on the bottom side. You can peek at it by gently lifting an edge with a spatula. Toward the end of this time, make certain it has not stuck to the pan by twisting the pan back and forth.

The traditional way of cooking the top side of this type of frocia is to turn it over onto a plate, then slide it off the plate back into the pan. I have found, however, that an easier method is not to turn it at all, but to simply place the pan in the broiler with the rack set at the greatest distance from the flame. If the handle of your pan is plastic, leave the door open with the handle sticking out so it doesn't melt. Cook it in this manner for only a few minutes and check it often, as it can easily burn.

This frocia may be served hot or at room temperature.