Stir in the ground chiles, cumin and Mexican oregano. Throw in the onions, garlic and tomato sauce. Add enough water to barely cover the mixture. Season to taste with salt and pepper. Stir the pot until the ingredients are well incorporated. Bring the liquids to a boil, cover, cut the heat to a slow simmer and braise for 1 - 1 1/2 hours. Stir the pot - on occasion. Thicken the chili with a slurry of cornstarch and water. The consistency of the chili should be thick - so as not to disintegrate the hot dog rolls. If the chili requires a boost in heat, add cayenne pepper or hot sauce to taste.
Cook the hot dogs to your liking. For chili dogs, I poach them (below the simmer) entirely covered with water - never allowing the water to simmer. Spread heaps of chili over the dogs in their rolls. Top with grated cheese. Serve mustard, hot sauce and chopped onions on the side.