Add potatoes to a large saucepan filled with salted water and bring to a boil. Cook until tender (about 15 minutes). Drain. Add potatoes to a large bowl and sprinkle with white vinegar. Stir in dill pickles and onions. Let cool.
Preheat oven to 400°F. Remove any loose layers from the garlic head. Cut the top of the garlic head to expose the cloves. Place on a sheet of aluminum foil and drizzle with olive oil. Bake for 40 to 45 minutes, until softened. Squeeze garlic into a bowl and mash with a fork. Set aside.
Preheat the BBQ to medium-high heat. Grill Smokies for about 8 to 10 minutes, turning often. Remove from grill and set aside to cool. Once cool to the touch, slice into 1/2-inch coin-sized pieces. Add to potato mixture.
Add mayonnaise, mustard, salt and pepper to the bowl with the garlic. Stir to combine. Pour over potato mixture and toss. Sprinkle on parsley and stir to combine. Refrigerate until ready to serve.