First prepare the dressing. Add the ingredients to a jar with a tight fitting lid and shake to combine. Refrigerate and let sit (shaking regularly) to blend the flavors.
Next add the cubed potatoes to a large pot of well salted water, covering the potatoes by about 1". Check the water to make sure it is just a little salty and add more salt if needed. *Make sure to use a large enough pot so the potatoes aren't crowded* Bring to a boil over medium-high heat with a lid on. Once boiling, remove the lid and reduce the heat to a slight simmer. Cook until the potatoes can be pierced with a fork but are not falling apart. About 5 - 6 minutes. Watch them closely so they don't get over-cooked.
When the potatoes are done, drain them in a colander and set aside to cool for about 10 minutes. After 10 minutes, remove the potatoes carefully to a couple baking sheets to continue cooling for another 5 minutes.
When the potatoes are cooled but still slightly warm, gently combine them the green onions, red onions, red bell pepper, capers, dill pickles, dill pickle juice, fresh dill, fresh parsley, salt and pepper to taste and the dressing. *NOTE: Start with 1/2 - 3/4 of the dressing first and taste.* The remainder of the dressing can be added after the salad chills. Stir it in just before serving.
Cover and refrigerate to chill and combine flavors for at least 2 - 4 hours.