Slice bacon and cook in a skillet until crisp. Drain, reserving 1/4 cup of bacon grease.

Crumble bacon and set aside.

Combine sugar and flour in the skillet with the reserved bacon grease.

Add vinegar, water, salt, and dry mustard to the skillet.

Add chopped onion and celery to the skillet.

Cook, stirring constantly, until the mixture thickens.

In a bowl, combine cooked and sliced red potatoes, shredded carrots, and parsley.

Pour the sauce over the potato mixture and stir gently to coat.

Season with additional salt and pepper to taste.

Serve hot or cold.