Grind the soaked urad dal with very less water. Add salt, peppercorns, cumin seeds and ginger. Mix well and keep aside.
Heat oil in a pan. Dip your hands in a bowl of water. Take a portion of the batter and give a round shape to it. Make a hole in the centre with your thumb.
Gently slide in the vada in hot oil and fry on a medium flame till it is golden and crisp. Immediately drop in a bowl of water and let them soak for a while. Then squeeze out the water by pressing in between your palms. Keep aside.
Grind the coconut and green chilies. Add in the yoghurt, some water to dilute it, salt, coriander leaves (save some for garnishing), grated carrot and chopped chili. Mix well.
Heat 1 tbsp. oil and temper with mustard seeds and dry red chili. After it stops spluttering, add the urad dal and curry leaves. Saute for a few seconds and switch off the flame.