Preheat the oven to 450 degrees F (230 degrees C). Cut each hot dog into 6 pieces. Pour egg, 2 tablespoons vegetable oil, sugar, and milk into a mixing bowl; whisk until combined. Add white vinegar, cornmeal, flour, baking powder, baking soda, kosher salt, and cayenne. Whisk briskly until ingredients are combined and batter is relatively thin and overmixed. Set batter aside for 10 minutes before using.
Bring a large pot of salted water to a boil, add linguini and return water to a boil. Let linguini cook until al dente; drain well. In a large skillet, saute the onion and garlic in olive oil until the onions are translucent. Drain the cans of minced clams, reserving half of the juice.
Place the potatoes into a large pot and cover with salted water. Bring to a boil, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Season the potatoes with salt, and mash with 6 tablespoons of butter, sour cream, egg, and milk.