Prepare the potatoes. Wash and peel the potatoes, then cut them into cubes measuring about 3/4-inch.
Cook until tender but firm. Transfer the potatoes to a large pot and cover them with water. Add the 1 tablespoon salt. Bring the water to a boil, reduce the heat to a simmer, and cook until the potatoes are tender while still firm enough to hold their shape.
Season the warm potatoes. Drain the potatoes, then immediately sprinkle them with the 2 tablespoons white vinegar.
Whisk the dressing. In a small bowl, combine the 2 teaspoons yellow mustard, 1/2 cup mayonnaise, and 3 tablespoons pickle relish. Whisk until the dressing is evenly mixed.
Bring the salad together. Place the potatoes, 3 large finely chopped hard boiled eggs, and 1/2 small minced sweet onion in a large bowl. Add the dressing and lightly toss until everything is coated.
Season and serve. Add salt and pepper to taste. Enjoy the salad warm, or refrigerate it for several hours to allow the flavours to develop further. After chilling, taste again and adjust the seasoning before serving.