Heat the oil in a large pot over medium heat until shimmering.
Add the chopped onion and sauté until it becomes soft and translucent, releasing a sweet aroma, about 5 minutes.
Stir in the minced garlic and cumin seeds, cooking for another minute until fragrant and slightly toasted.
Add the chopped tomatoes and turmeric, cooking until the tomatoes break down and the mixture thickens slightly, approximately 8 minutes.
Stir in the diced potatoes, coating them well with the spice mixture, and cook for 2 minutes to start softening the potatoes.
Crumble in the dried lime or add lime juice, then pour in water, stirring to combine everything evenly.
Bring the mixture to a gentle boil, then reduce the heat to low, cover, and simmer for about 30 minutes, or until the potatoes are tender and the sauce has thickened, stirring occasionally.
Uncover and season with salt and pepper to taste. Continue cooking uncovered for another 5 minutes to allow any excess liquid to reduce slightly.
Turn off the heat and let the dish rest for a couple of minutes; the potatoes will absorb the flavors, and the sauce will become velvety.
Serve the Dopiazeh Aloo hot, garnished with fresh herbs if desired, accompanied by rice or bread for a complete meal.