Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes.
Drain and let cool.
Mix dry mustard with 1 teaspoon water in a small bowl and let stand 10 minutes to develop flavor.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes.
Drain the bacon slices on paper towels. Reserve bacon drippings in skillet.
Let bacon cool; crumble bacon.
Cook onion in reserved bacon drippings over medium heat until onion is translucent and soft, about 5 minutes. Stir mustard paste, sugar, 1/4 cup water, and cider vinegar into onion; bring to a boil. Reduce heat to low and simmer vinegar dressing for 2 minutes.
Peel potatoes if desired; slice 3 potatoes into a salad bow and arrange into a layer.
Sprinkle potatoes with half the crumbled bacon, celery, and parsley; season with salt and black pepper.
Pour a little of the vinegar dressing over the layer. Repeat layer with remaining 3 potatoes, bacon, celery, parsley, salt, and black pepper; pour remaining dressing over the salad. Cover and let stand at room temperature for 30 minutes before serving.
