Combine the diced Yukon gold potato, diced pumpkin (or ash gourd), chopped carrot, drumstick sections, and 2 cups of water in a pot. Bring it to a boil over high heat and cook for about six minutes until the potatoes are fork-tender.

Remove the seeds from the tindora using a sharp spoon, and then chop the tindora into 1 cm pieces. 

Add the diced green plantain, salt, chopped cucumbers, green beans, chopped tindora, and curry leaves to the pot. Stir well and continue to cook for an additional five to seven minutes until the vegetables are tender yet retain their shape.

While the vegetables are cooking, prepare the coconut paste. In a blender, combine the unsweetened shredded coconut, grated fresh ginger, cumin powder, green chilies, and 1 cup of water. Blend on high speed for 90 seconds until you achieve a smooth paste-like consistency.

Add the coconut paste, lime juice and yogurt to the pot with the cooked vegetables. Mix well to combine and allow it to simmer on low heat for another three minutes.

In a separate small pan, prepare the tadka (tempering). Heat the coconut oil or vegetable oil over medium heat. Add the brown mustard seeds and urad dal and allow them to crackle and pop. Then, add dried byadgi chilies, curry leaves, and asafoetida. Stir fry for a minute or until the dal turns golden brown. 

Place the aviyal into an attractive serving dish and top it with the tadka. Garnish, if desired, with fresh cilantro leaves. If you want a more colorful aviyal, simply add a half teaspoon of turmeric powder to the coconut gravy.