Grate the cucumber using a box grater or finely dice it. Place in a clean kitchen towel and squeeze out excess water. Transfer to a mixing bowl.
In a small bowl, whisk the yogurt until smooth and creamy. Add the yogurt to the cucumber along with cilantro, mint, green chili, salt, cumin, and chaat masala. Stir well to combine.
Make the tadka: Heat oil or ghee in a small skillet over medium heat. Add mustard seeds and cook until they start to pop, about 30 seconds. Add dried red chilies, curry leaves, and asafoetida. Cook for 10 seconds until fragrant, then remove from heat.
Immediately pour the hot tadka over the salad and stir to incorporate. Taste and adjust salt or spice as needed.
Cover and refrigerate for at least 30 minutes to allow flavors to meld. Garnish with extra cilantro and mint before serving.