Slice the small potatoes in half, or in quarters if larger. Place them in a large pot and cover with 1 inch of water. Add 1 tablespoon of salt and bring to a boil over medium-high heat. Once the water is boiling, reduce the heat to medium and simmer for about 15 minutes until fork-tender. Drain immediately and briefly rinse under cold water. (Don't rinse long enough to cool the potatoes.)
1.5 pounds small potatoes (gold, red-skinned or a mix), 1 tablespoon salt
While the potatoes are cooking, combine the EVOO, red wine vinegar, salt, and pepper in a large bowl. Beat vigorously with a whisk to blend and emulsify. Add Dijon mustard, grainy mustard, 3 tablespoons of the freshly chopped dill, diced shallots, capers, and caper juice. Stir to combine.
2 tablespoons Extra Virgin Oil Oil, 1 tablespoon red wine vinegar, 1 tablespoon Dijon Mustard, 1 tablespoon Grainy Mustard, 1 tablespoon salt, ¼ teaspoon freshly ground black pepper, 4 tablespoons fresh dill, 1 medium shallot, 1 tablespoon capers, ½ tablespoon caper juice
Add the cooked and rinsed potatoes to the bowl of vinaigrette. Toss gently to coat the potatoes with vinaigrette. Taste and season if needed.
Serve warm or chilled. Sprinkle with the remaining 1 tablespoon of freshly chopped dill before serving.