Heat vegetable oil in a large pot over medium heat until shimmering. Add the chopped onion and cook, stirring frequently, until it becomes translucent and fragrant, about 5 minutes.
Add the minced garlic and cook for another minute until it releases a rich aroma. Sprinkle in the ground cumin and stir to coat the onions and garlic evenly, about 30 seconds.
Pour in the chopped ripe tomatoes and stir well. Cook the mixture, stirring occasionally, until the tomatoes soften and the sauce begins to thicken, approximately 10 minutes, filling the air with a tangy aroma.
Add the sliced potatoes to the tomato mixture, spreading them evenly in the pot. Pour in enough water to just cover the potatoes, then season with salt and pepper to taste.
Bring the contents to a gentle boil, then reduce the heat to low. Cover the pot and let it simmer quietly for about 30 minutes, or until the potatoes are tender and begin to break down, thickening the sauce nicely.
Uncover the pot and gently fold in the chopped fresh herbs, allowing their fragrant freshness to mingle with the stew. Continue simmering uncovered for another 5 minutes to develop a rich, flavorful sauce.
Taste and adjust seasoning with additional salt and pepper if needed. The sauce should be thickened, and the potatoes tender with a slightly broken texture, infused with the warm spice and tomato flavors.
Serve the Dopiazeh Aloo hot, with crusty bread or rice on the side, allowing the vibrant, herby sauce to envelop each bite.