Add the potatoes and 1 tablespoon salt to a large pot and cover with water. Bring to a boil and simmer until the potatoes are tender, about 10 minutes. Drain and set aside.
Put a large skillet over medium-high heat. Add the bacon and cook until crisp, 8 to 10 minutes. Transfer to a paper towel and leave the bacon fat in the skillet (it should be a nice thin even layer; pour some off if it's more than that).
Add the shallots to the skillet and cook until soft, 5 to 7 minutes. Add the stock, vinegar, pickle brine, mustard and sugar and cook, whisking, until reduced by about a third and slightly thickened, about 7 minutes.
Fold in the potatoes to coat evenly. Chop the bacon and add to the potatoes. Add the scallions, parsley, a bunch of black pepper and salt to taste. Serve warm or at room temperature.