Rinse the split white Urad Dal under cold water. Place the rinsed dal into a bowl and cover it with four cups of water. Soak the dal for a minimum of two hours to a maximum of five hours. Drain the water before proceeding.
In a blender or food processor, grind the soaked Urad Dal and ⅓ cup of cold water into a smooth paste. You will likely need to stop blending intermittently to scrape the insides of the bowl down to ensure there are no whole pieces of dal left. The batter should be thick, sticky, and smooth.
Transfer the Urad Dal batter to a mixing bowl. Add salt, black pepper, diced red onion, chopped cilantro leaves, minced green chili, grated ginger, chopped curry leaves, asafetida, and chopped mature coconut meat (if using). Mix well to incorporate all the ingredients.
Heat oil in a deep fryer or deep pan on medium heat to a temperature between 350-360. Wet your hands with water to prevent sticking and take a small portion of the batter and shape it into a rounded donut shape with a hole in the center. Try to hold the vadai more in the palm of your hand than in the area of your hand with your fingers, so that your fingers do not create impressions in the soft bottom side of the batter.
Carefully slide the shaped vadai into the hot oil. Fry them in batches, ensuring not to overcrowd the pan. Fry until they turn golden brown and crispy on both sides. It should take about four minutes to cook.
Using a metal spider or slotted spoon, remove the fried vadai from the oil and place them on a wire rack to drain excess oil.
Serve the vadai hot and crispy as a standalone snack or with chutneys and sambar for a complete meal.