For the cake, whisk the eggs and sugar in a sizable bowl until thoroughly mixed.
Add the pineapple, carrots, oil, pecans, baking powder, baking soda, cinnamon, and vanilla extract.
Mix until well mixed.
Add flour and mix until it is well mixed.
Pour into a pan.
Bake for 30 minutes or until a wooden pick inserted in the centre comes out clean.
On a wire cooling rack, keep it for at least 2 hours.
For Icing
For the icing, a bowl of medium size beat together sugar and butter until creamy.
Add vanilla extract and cream cheese and beat until smooth and smooth.
Sprinkle with pecans and carrots.
Notes
Before icing the cake, let it cool fully. For the best shape, arrange the top layer right-side up on a plate and the bottom layer upside-down. Brush the cake lightly to get rid of any stray crumbs.
Before icing the entire cake, spread a thin coating of icing on the sides to "set" any crumbs that may still be there.
Adjust the baking time when baking a loaf or cupcakes so a wooden toothpick put into the centre comes out clean.