Preheat oven to 350ºGrease two 9" cake pans (brush on oil or use a nonstick spraand then also line the bottoms with parchment paper.
Whisk the eggs in a large bowl until pale and blended, then whisk in the carrot, oil and buttermilk.
In a separate large bowl, whisk together the flour, sugar, baking powder, baking soda, spices and salt.
Scrape the carrot mixture into the dry ingredients.
Use a rubber spatula or wooden spoon to fold the carrot mixture into the flour mixture until just blended. Stop as soon as no dry flour remains.
Use a spatula to scrape the batter evenly between the two prepared pans.
Bake for about 35 minutes, or until you gently press the centre and it feels a bit bouncy, rather than your finger sinking in.
Let the cake layers cool in the baking pans for 10 minutes to firm up slightly. Working with one pan at a time, run a butter knife around the outside of the cake. Place a cooling rack on top the cake pan, then (wearing oven mittflip the whole thing over in one motion (cake and cooling rack together). Repeat with second cake and let cool completely before frosting.