In a small mixing bowl, using a fork, beat the flax seeds together with the milk for about a minute. Add the vinegar, water, maple syrup, oil and vanilla. Mix well.
In a large bowl, sift together flour, baking powder, salt, and spices. Make a well in the center and add the wet ingredients. Mix with a wooden spoon just until combined. Fold in grated carrot. Let batter rest for at least 5 minutes.
Preheat a large non-stick pan over medium heat. Lightly coat pan with cooking spray or oil. Add batter in scant 1/4 cup scoops. I use an ice cream scooper for this and it works magically. Cook three at a time for about 4 minutes (or until the tops look mostly cooked), then flip and cook until lightly browned, 2 more minutes.
Keep on a plate covered with tin foil until ready to eat. Serve with pure maple syrup.