In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, mix the buttermilk, egg, brown sugar, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the grated carrots and chopped walnuts.
Heat a griddle or non-stick skillet over medium heat. Grease lightly with butter or oil.
Pour ¼ cup of batter onto the griddle for each pancake. Cook until bubbles form on the surface, then flip and cook until golden brown on the other side.