Place the potatoes in a pot with enough water to cover, and bring to a boil. Cook for about 20 minutes, or until tender. Drain and cool.
Meanwhile, place eggs in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover, and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, and place in a bowl of cold water to cool.
Peel the eggs, and place 3 of them into a large bowl. Reserve the rest for later. Mash the eggs in the bowl with a fork. Stir in the mustard, mayonnaise, celery, salt and pepper. Set aside.
Cook bacon slices in the microwave for about 4 minutes, until crisp, or fry in a skillet over medium-high heat. Crumble 2 of the bacon slices into the mayonnaise mixture. Reserve the rest for garnish.
Peel and chop the potatoes, and stir into the bowl until evenly coated. Slice the 2 remaining eggs, and place on top of the salad. Crumble the remaining bacon over the eggs, then sprinkle parsley over the top.