In a 10-inch heavy skillet, cook bacon over medium heat until browned and crisp. Remove bacon from pan with a slotted spoon and drain on a paper towel. Pour off all but 3 tablespoons of bacon drippings.
To the remaining drippings add potatoes and onions. Saute over medium low heat, stirring occasionally, until potatoes and onions are tender. Add more bacon drippings if necessary.
In a small bowl, lightly beat eggs with salt and pepper. Add the parsley and bacon.
Pour over potatoes and onions in skillet. Cover and cook over low heat until eggs are set, for about 5 to 6 minutes.
Sprinkle with cheese, if desired.
To serve, turn out onto a large platter and cut into wedges.