In a large bowl, combine flour, sugar, baking soda, baking powder, and salt; set aside.
In a separate bowl, whisk together eggs, syrup, applesauce, milk, and vanilla.
In a microwave safe dish, melt the coconut oil and then add it into the egg mixture.
Fold the wet ingredients into the dry ingredients.
Grease two 8-inch pans with coconut oil and then pour cake batter evenly in each pan, dropping the pans a couple of times on the countertop to even out the batter.
Place cake pans in the oven and bake for approximately 30 minutes, using a toothpick to test doneness.
For the icing: combine powdered sugar, orange juice and milk in a bowl and stir with an electric mixer. The icing should be VERY thick but still spreadable; if it's not thick, it will drip everywhere and be a hot mess (I know from experience).
Once the cakes are done, remove them from the oven but leave them in the cake pans for 10 minutes or so, allowing time for them to cool off before transferring to a cooling rack to cool completely.
Once the cakes have cooled, remove the top "dome" layer of one of the cakes with a knife and, using a spatula, ice the top of that cake before placing the second cake overtop, using the icing to "glue" the cakes together.
Next, use a spatula to ice the rest of the cake. You will most likely have extra icing and that's ok--better to have extra than not enough.
Once the cake is iced, place in the refrigerator for 30 minutes before serving.
Cut and enjoy!
*For more specific cake building instructions, consult Martha Stewart with the link I provided in my blog post titled How to Assemble a Layer Cake