To make the sauce, mix the mayo, mustard, chili paste, relish, and ketchup in a small bowl. Set aside in the fridge until ready to use.
Preheat oven to 350° F.
Using a fork, poke a few holes into each potato. Rub the potato with olive oil and salt and place on a baking sheet. Bake the potatoes for about an hour until tender.
Preheat about 3 inches of vegetable oil in a heavy bottom pot to 375° F.
Peel the potatoes and run them through a potato ricer into a large bowl.
Add the scallions, parmesan, egg, and breadcrumbs. Stir well to combine. Add in the sour cream, starting with about half, and stir to combine. Add more as needed until the mixture is smooth but not too wet, it should be stiffer than mashed potatoes.
One by one, stick a popsicle stick into a hot dog starting at the cut end, and putting it about 3/4 of the way through the dog.
Take about 1/4 cup of the potato mixture in your hand and press it flat into your palm. Wrap it around the hot dog, adding more as needed. press it to tightly seal. Repeat until you run out of the potato mixture or the hot dogs.
In a few batches, fry the potato dogs, flipping a few times to evenly brown on all sides. Remove from oil to a drying rack or paper towel and season with a pinch of salt.
Serve the potato dogs with the sauce on the side, or drizzled on top if desired.