1. Place the potatoes in a large pot and cover with cold water by 1 inch. Bring to a boil over medium-high heat. Cook the potatoes until they fall off a fork easily, 20 to 28 minutes; drain and set aside. When cool enough to handle, slice the potatoes in half.
2. In a large bowl, mix together the mayonnaise, gherkins, gherkin juice, mustard, salt and pepper to form a dressing. Add the potatoes, the red onions and eggs, and gently fold together to coat with dressing. Taste, and adjust the seasoning as needed. Garnish with parsley and paprika.