Put taro into a large pot, fill pot with cold water, and boil over high heat until tubers are completely soft when pierced with a fork, about 50 minutes. Drain, set taro aside to let cool until just cool enough to handle but still hot, then peel. Put taro on a work surface and flatten each tuber slightly with the bottom of a large flat plate or dish. The tubers may crack around the edges but should not fall apart.
Heat ghee in a small heavy pot over medium heat until a slice of the onion sizzles instantly when dropped into the pot. Fry onions, stirring often with a slotted spoon, until dark brown but not burned, about 8 minutes. Transfer onions to paper towels to let drain and cool. Chop onions finely and set aside.
Working in 2–3 batches, fry taro in same pot of ghee over medium heat, turning once, until golden brown, 10–12 minutes per batch. Drain on paper towels as done. Discard all but 4 tbsp. of the ghee.
Put garlic and ginger into a blender and, with motor running, drizzle in 4–5 tbsp. cold water through hole in blender lid, blending until a loose paste forms.
Heat the reserved ghee in a large skillet over medium heat. Add garlic–ginger paste and fry for 2–3 minutes. Add onions and fry for 1 minute. Stir in chile powder and 2 cups cold water, then yogurt, and bring to a simmer. Reduce heat to a medium-low and gently simmer until slightly thickened, 20-25 minutes. Add garam masala and season to taste with salt. Add taro and simmer until tubers have absorbed some of the sauce and are completely heated through, about 10 minutes. Transfer to a serving dish.