Heat vegetable oil in a pan over medium-high heat.
When the oil is hot, add asafoetida (hing), nigella seeds (kalonji), and fennel seeds (saunf), and let them crackle for 4-5 seconds.
Add the mangoes wedges, salt, and Kashmiri red chili powder to the pan and mix well.
Stir in water and cover the pan with a tight-fitting lid.
Cook for 10-12 minutes until the mangoes are softened. Stir a few times while cooking. Now add 1 and ½ cups of crumbled jaggery and cook till it melts, stirring continuously.
Cover the pan once again and cook for 3-4 minutes.
Remove the pan from heat and let the launji come down to room temperature. Serve at room temperature or chilled.