Preheat oven to 350 degrees.
Beat together eggs, oil, white sugar and 2 teaspoons vanilla.
Mix in flour, baking soda, baking powder, salt and cinnamon.
Stir in carrots.
Stir in pecans.
Fill cupcake tins and bake for 22-26 minutes, or until a toothpick inserted in the middle of the cupcake comes out clean. For a 9 x13 cake, I would cook same temp for 30-45 mins or until a toothpick inserted in the middle of the cupcake comes out clean.
Time to make the frosting. Beat butter, vanilla extract and powdered sugar together.
You may need to add a couple tbsp of milk or water to the mix to help the frosting come together.