Cut the vegetables into even batons. Keep firmer pieces (yam, raw banana, carrot, drumstick) in one pile and quicker-cooking pieces (pumpkin, cucumber, brinjal) in another if you want staggered cooking.

Grind coconut, cumin seeds, and green chili with just enough water to make a thick, coarse paste. Set aside.

In a heavy pot, add the firmer vegetables with turmeric, salt, and about 3/4 cup water. Cover and cook on medium heat for 8 to 10 minutes. Add the softer vegetables and cook 5 to 7 minutes more, until everything is tender but not mushy. Add a splash of water only if the pot is dry. If a lot of liquid remains, uncover and simmer until it looks lightly moist, not soupy.

Stir in the coconut paste. Simmer 3 to 4 minutes on low heat so the raw coconut taste softens and the gravy coats the vegetables.

Whisk the coconut yogurt with 2 tablespoons of the warm gravy or paste in a small bowl until smooth.

Turn off the heat. Wait about 30 seconds, then fold the yogurt mixture into the pot gently. Taste and add a spoon more yogurt or salt if needed.

In a small pan, heat coconut oil. Add mustard seeds and let them pop. Add curry leaves and dried red chili if using. Pour the tempering over the avial. Garnish with coriander if you like. Serve warm with rice.