In a large pot with a lid, heat the oil over medium-high. Add the beef and onion; season with salt. Cook, stirring often and breaking up with a spoon, until the beef is browned and cooked through, about 5 minutes. Drain any fat. Stir in the tomato paste and spices; season with pepper. Stir in the ketchup, stock, vinegar, sugar, and Worcestershire. Cover and reduce heat to low. Simmer the chili, stirring occasionally, until the flavors meld, about 20 minutes.
While the dip cooks, preheat the oven to 350 degrees. Brush the cut sides of the hot dog buns with mustard. Cut the hot dog buns into thirds and transfer to a baking sheet. Bake until toasted, about 6 minutes. Top the dip with cheddar, pepperoncini, white onion, and a squiggle of mustard. Serve with the toasted hot dog buns and pigs in blankets.