Powder the toasted sesame seeds in a coffee grinder or blender.
Put the raw mango pieces with the turmeric and a little salt in a pan and cook for about 10 mins on low heat. The mangoes will release their juices and and become soft and mushy. Cool.
In a food processor, grind the mango with the powdered sesame, mustard seeds, fenugreek seeds, green chillies, garlic and salt (as needed), till you have a thick, paste. Do not use water.
Transfer the pachadi to a bowl. Heat oil in a pan and when it's hot, add the mustard seeds, cumin seeds, urad dal and curry leaves till they crackle. Take the pan off the flame and add the asafoetida and red chilli. Pour the tempering over the pachadi andmix well. Store in the fridge for 3-4 days.