Warm the oil in a large Dutch oven or deep skillet over medium heat. Add the onion and cook, stirring often, until softened and lightly golden, about 8 to 10 minutes.
Stir in the garlic, ginger, optional chile, turmeric, cumin, salt, and black pepper. Cook for 30 seconds, just until fragrant.
Add the potatoes and carrots, tossing them well in the spiced onion mixture. Add the water or vegetable broth and bring it to a gentle simmer.
Pile in the cabbage, cover the pot, and cook for 10 minutes. The cabbage will shrink substantially as it steams.
Uncover, stir everything together, cover again, and cook for 10 to 15 minutes more, stirring once or twice, until the potatoes and carrots are tender and most of the liquid has cooked away. Add a small splash of water if the pot becomes dry before the vegetables are done.
Taste and adjust the salt. Serve hot as a vegetable side dish, or spoon it over rice with a protein or lentils for a simple meal.