Combine mung beans, fenugreek seeds, and 3 cups water in a bowl; let sit 5 hours, then drain and transfer to a food processor. Add cilantro, rice flour, cumin, asafoetida, turmeric, chiles, ginger, salt, and 1 cup water; purée into a smooth batter. Heat a 12″ nonstick skillet over medium-high. Brush skillet lightly with oil. Using a ladle, pour ⅓ cup batter into center of pan.
Immediately and in a circular motion, spread batter from center toward edge of pan, creating a thin, 7″ pancake. Drizzle 1–2 tbsp. oil around edges and on surface of pancake. Cook, covered, until golden, 1–2 minutes. Flip pancake and cook, uncovered, until golden, about 1 minute more; slide onto a plate. Repeat with remaining batter, brushing skillet with oil between pancakes. Serve with cilantro-yogurt chutney, if you like.