Wash hands with soap and water.
In a medium bowl, mix oats and buttermilk and set aside to soak.
In a medium bowl, add egg, oil, milk, and vanilla extract, beat well. Stir in the carrot.
In another medium bowl, stir together dry ingredients.
Add the carrot mixture to the oat mixture. Stir well.
Add dry ingredients to the oat and carrot mixture and stir gently. If it seems too thick, add a small amount of milk.
Lightly grease a large skillet or griddle and heat over medium-high heat (350 degrees F in an electric skillet). For each pancake, pour about ¼ cup batter onto the hot skillet or griddle.
Cook until bubbles come to the surface of the pancake and the edges begin to dry. Turn over and cook other side until golden brown.
Refrigerate leftovers within 2 hours.