Stir water, ground hot dogs, vinegar, paprika, chili powder, sea salt, red pepper flakes, onion powder, oregano, cinnamon, white pepper, thyme, and black pepper together in a large stockpot; bring to a boil, reduce heat to medium-low, and simmer for 45 minutes.
Stir cornstarch with just enough cold water to dissolve completely; stream into the hot dog mixture while stirring. Continue to cook, stirring frequently, until the sauce has thickened slightly, about 15 minutes more. Adjust salt and pepper to taste before serving.
