Firstly, mill the flour. I used soft white wheat, if you are using a different wheat variety you may need a little less flour.
Then, peel and shred the carrots, and chop any nuts you will be adding to the carrot cake. Set these to the side.
To the freshly milled flour add sugar, brown sugar, baking soda, baking powder, salt, ginger, cinnamon, and nutmeg. Mix these ingredients together until incorporated.
Then, to a stand mixer, add the melted butter and oil mix to combine.
Add eggs one at at time, mixing between each one.
Then, add the yogurt and vanilla, mix to combine.
Now it is time to add in the flour mixture, slowly mix until just incorporated. Scrape sides as needed.
Add in the shredded carrots, and any other mix-ins like nuts or raisins. Stir to mix in evenly. Scrape sides as needed here too.
Preheat the oven to 350*F. (While the oven preheats, I like to let the batter sit just a bit, so the freshly milled flour has time to absorb the liquids.)
Prepare your baking pans. Trace the bottom of your pan with a pencil and parchment paper, then cut the circles out. Spray your baking pan with baking oil, then place the parchment paper circle in the pan, and spray it again. Be sure to get the oil up the sides of the pan as well.
After the oven is preheated, and your pans are prepared. Divide the batter evenly into each 8x8 round cake pan.
Bake the cakes for 38-42 minutes. Check to make sure a toothpick comes out clean from the center. (Some moisture and crumbs are ok on the toothpick, just don't want raw batter.) When the cake edges start to pull away form the edge of the pan, the cake is done. Don't overbake, it can make it dry. (If you have different size cake pans, your baking time will change. See notes)
Once the cakes are baked, let them cool in the baking pan for 10 minutes. Then run a knife around the cake to make sure it hasn't stuck to the sides of the pan for easier removal.
Turn the cakes out of the pan onto a wire cooling rack. Then, let the cakes cool completely before frosting.
While the cake is cooling, make the cream cheese frosting.