Heat the oil in a large nonstick skillet over medium heat. When the oil is shimmering, add the ginger, garlic, carrots if using, onions and sprinkle with salt and pepper. Cook until the onions are softened and slightly brown around the edges, about 5 minutes.
Add the turmeric, paprika and garam masala and stir quickly, about 20 seconds. Stir in the ketchup and tomatoes, and taste for seasoning; add more salt and pepper if needed.
Add the hot dogs, stirring to cover them with the tomato mixture. Add 1/4 cup water if the mixture is too dry. Cover the skillet and simmer over medium-low heat, about 15 minutes.
Taste the hot dogs and season accordingly. Remove the skillet from the heat. Stir in the cilantro and transfer the mixture to a serving bowl or serve in the pita bread.