Dry-roast the peanuts in a skillet over medium heat, stirring often, until golden and fragrant and the skins begin to split, 6–8 minutes. Transfer to a plate to cool for 5 minutes, then rub between your palms to shed any loose skins (optional for a smoother chutney).
Transfer them to a blender with the green chilies, garlic, tamarind paste, fine salt, and 0.5 cup of the water. Blend until smooth, 45–60 seconds, scraping down as needed; add the remaining water as needed (up to 0.25 cup more) to reach a medium-thick, spoonable consistency. Scrape the chutney into a serving bowl.
For the tempering, heat the peanut oil in a small pan over medium heat. Add black mustard seeds; when they crackle and pop, 30–45 seconds, add urad dal and fry until pale golden, 30–60 seconds. Add the dried red chile, curry leaves, and asafoetida; fry just until the leaves crisp and the spices smell nutty, 10–15 seconds.
Immediately pour the hot tempering over the chutney and stir to combine. Taste and adjust salt. Serve with idli, dosa, vada, or uttapam.