Step 1

In a large saucepan, cover the potatoes with water and bring to a boil. Add a generous pinch of salt and simmer over moderate heat until tender, about 20 minutes. Drain the potatoes in a colander, shaking off any excess water.

Step 2

Meanwhile, in a large skillet, cook the bacon over moderately high heat, stirring occasionally, until crisp, about 8 minutes. Using a slotted spoon, transfer the bacon to paper towels to drain. Pour off all but 2 tablespoons of the fat from the skillet. Add the onion and cook over moderate heat, stirring, until just starting to brown, 6 to 8 minutes. Add the vinegar, mustard and celery seeds and cook, stirring, until most of the liquid has been absorbed, about 2 minutes.

Step 3

In the large saucepan, melt the butter in the milk over moderately low heat. Remove from the heat. Press the potatoes through a ricer into the pot and mix well. Fold in the mayonnaise, bacon, onion mixture, and parsley and season with salt and white pepper. Serve right away.