Place the buckwheat and water in a covered bowl or jar and leave out overnight.
In the morning, puree buckwheat with the carrot. Pour into a medium size bowl and combine with the rest of the ingredients. Once you have combined everything, don't stir it again. Just spoon gently onto the skillet to help maintain the fluffiness. If the batter seems a little thick to you, add a little water or vegan milk. I would try making a pancake first before adding more liquid.
Heat a pancake skillet on medium low. Add a little oil to barely cover the surface. The skillet is ready when a small drop of water lightly dances on the surface. Take care to not get it too hot. Spoon batter in small circles onto skillet. Let cook. These pancakes will get a few bubbles on top when they are ready to turn. Turn over and cook the other side for a minute or two. Transfer to a plate in a warm oven. Continue to make pancakes until batter is gone.
Serve with your favorite pancake toppings.