Bring the vinegar, sugar, mustard seeds and 1 tablespoon salt to a boil in a small saucepan and cook until the sugar and salt dissolves, about 1 minute. Transfer to a small bowl and let cool for 10 minutes. Add the onions and stir to combine. Cover and refrigerate for at least 1 hour and up to 24 hours. Drain the onions through a strainer into a bowl and reserve the pickling liquid.

Put the potatoes in a large pot, cover with cold water by 2 inches and add 2 tablespoons salt. Bring to a boil over high heat and cook until a knife inserted into the center of the potatoes meets with no resistance. Drain the potatoes well, let cool slightly (but not all the way) and slice into 1/2-inch thick slices.

Transfer the warm potatoes to a large bowl. Add the eggs, pickled onions and red peppers. Whisk together the mayonnaise, mustards, a few tablespoons of the pickling liquid and season with salt and pepper. Add the dressing and parsley to the warm potatoes and gently mix to combine; season with salt and pepper. Serve at room temperature or cover tightly and refrigerate for at least 2 hours and serve chilled.