Heat oil in a large pot over medium heat. Add carrots and sauté until slightly softened, about 5 minutes. Add onion; sauté until fragrant, about 2 minutes. Add turmeric, cumin, salt, pepper, and ginger; let seasonings toast until fragrant, about 1 minute.

Stir cabbage and garlic into the pot; cook, stirring occasionally, until cabbage wilts, about 10 minutes. Stir in potatoes and water; bring to a boil. Reduce the heat to medium-low and simmer, stirring every 10 minutes, until potatoes are tender, about 30 minutes.