I'm choosing to call this "Vegan Swing" cake because it can be made oil free and vegan or not, just by switching out two of the ingredients. This is based on Tammy Elliot's carrot cake recipe on AllRecipes.com.
2 cups flour
2 tsp baking powder
2 tsp baking soda
1/2 tsp salt
1 tbs cinnamon
1/4 tsp nutmeg
4 eggs or Ener-G Egg Replacer
1 1/4 cups vegetable oil or plain unsweetened apple sauce
1 cup white sugar
1 cup brown sugar
1 tbs vanilla
3 cups grated carrots
1 cup raisins
1. Start by grating your carrots. I used most of a 1lb bag.
2. Sift together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
3. Mix together your eggs (fake or otherwise), oil or applesauce, sugars, and vanilla. I used 1/2 cup of oil and 3/4 cup of apple sauce in this particular cake and it turned out well. You can fuss with the proportions as much as you want.
4. Sift your dry ingredients into your wet ingredients and mix together.
5. Stir your carrots into the batter.
6. Add your raisins.
(Or don't. Probably don't. Raisins should not be in cake. They should be in cookies.)
7. Oil and flour two 8" round cake pans. If you're going oil free flour alone should be fine.
8. Pour half your batter into each pan. Bake at 350 for 30 minutes. Swap pan positions in the oven halfway through for even baking.
9. Cool in the pans for 15 minutes or so then turn them out onto a cooling rack. Observe the echinacea tea photobombing in the background.
10. Find some frosting.
11. Take your cake outside for some inexplicable reason and plop half a can of frosting on one of the layers. Spread it out.
12. Put the other cake layer on top of the frosting. It will now look like a giant whoopie pie.
13. Plop another half can of frosting on top of this layer.
14. Spread it out.
15. Cover the sides with more frosting so they don't feel left out.
That's it, folks! You now have a delicious carrot cake that may or may not be vegan. Throw some candles on top of that thing and have yourself a party.