Preheat oven to 325 degrees F and butter two round cake pans, or an 8x8 baking dish. Add flour to coat, then shake out excess and set aside.
In a large mixing bowl, prepare flax eggs by mixing flaxseed and water and let rest.
Core apples (no need to peel) and grate. I recommend a mix of finely grated, and coarsely grated. Place grated apple on a clean dish towel and gently squeeze to remove about half of the juice. Set aside. (P.S. you should totally drink that apple juice.)
To the flax egg, add sugars, molasses, oil, vanilla, almond milk, grated apples, and whisk.
Set a sifter over something to catch fall out and add dry ingredients in this order: 1 cup whole wheat flour, baking soda, baking powder, salt, ginger, cinnamon, remaining 1/2 cup whole wheat flour. Stir gently with a spoon, then sift over wet ingredients and stir to combine, being careful not to over mix).
Lastly, add oats and stir again to combine, being careful not to over mix. The batter should be thick but pourable. If it appears too thick, add a bit more almond milk to thin and stir.
Pour batter into prepared cake pan(s). If you're dividing between two pans, it may look like there’s not enough batter but there is! Spread it in an even layer and it will rise while baking.
Bake for about 30-35 minutes if using 2 round cake pans, or about 40-50 minutes for an 8x8. A toothpick inserted into the center should come out clean and the edges should be visibly browned. Remove from oven and set out on counter to cool completely.
While the cake is cooling, prepare frosting. To the same mixing bowl (rinsed clean), add softened cream cheese, softened butter and beat or whisk vigorously to combine. Then add powdered sugar in 1/2 cup increments until thick and spreadable.
Add flour at the end to thicken (optional - or just more powdered sugar). You want this frosting to be pretty thick so it won’t slide off the cake, so keep adding flour and/or powdered sugar until it reaches the right consistency.
Once the cake is completely cooled, add 1/3 of the frosting to the top of the bottom layer and spread into an even layer. Then add the top layer of cake and frost generously with remaining frosting, coating sides last. Add crushed pecans on the edges (optional), slice and serve.
The cake should be stored covered in the fridge for optimal freshness, and should keep for 3-4 days. Move to the freezer after that, and thaw at room temp before serving.