Heat oil in a large saucepan over medium heat. Add onion; cook and stir until soft, about 10 minutes. Stir in ginger-garlic paste and chile peppers; cook until fragrant, about 1 minute.

Stir tomatoes, coriander, cumin, turmeric, and salt into the saucepan; mix well. Add turnips and hot water; stir well. Cover and bring to a boil. Reduce heat and simmer until turnips are tender, 20 to 30 minutes. Add brown sugar and coarsely mash the turnips.