1. Place potatoes in a large saucepan; cover with water. Bring to a boil. Reduce heat; simmer 15 minutes or until tender. Cool 10 minutes; peel and chop. Combine potatoes, onion, celery, carrot, and chopped eggs in a large bowl.
2. Cook bacon in a large nonstick skillet over medium heat until crisp, stirring occasionally. Remove bacon from pan with a slotted spoon, reserving 2 tablespoons drippings in pan. Combine sugar, 1/2 cup water, white vinegar, and next 5 ingredients (through beaten eggs); stir with a whisk. Add sugar mixture to pan; cook 8 minutes over medium heat or until slightly thick, stirring constantly with a whisk. Pour sugar mixture over potato mixture, stirring gently to combine. Add reserved bacon and parsley; toss gently to coat. Serve warm or at room temperature.