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Combine ½ cup mung beans and ½ cup rice in a fine-mesh sieve and rinse under cool running water until water runs clear. Transfer to a large Dutch oven or other heavy pot (the larger the better, this bubbles vigorously) and add 1 bay leaf, 1 tsp. peppercorns, 1 tsp. turmeric, 1 tsp. salt, and 6 cups water.
Bring to a boil over high heat, then reduce heat to medium and cover pot. Cook, scraping down sides and giving mixture a stir 15 minutes in, until mung beans and rice are tender and mixture resembles a stew, 20–25 minutes. (If your pot lid is threatening to blow, feel free to crack it open slightly.) Remove from heat; taste and season with more salt if needed. Let sit, still covered, while you make the spiced ghee. (Alternatively, you can make this in an Instant Pot. Cook on rice setting on low-pressure 12 minutes and naturally release pressure.)
To make the spiced ghee, melt ¼ cup ghee in a small skillet over medium-high. Add 2 tsp. cumin seeds and cook until seeds start to sputter and brown, a matter of seconds. Remove from heat and immediately mix in 2 dried red chiles, __ 1 pinch asafetida__ (if using), and 1 pinch red chili powder.
Divide khichdi among bowls and add some spiced ghee to each.