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Step 1
Preheat the oven to 350 degrees F.
Step 2
Grease two 5 or 6 inch cake pans or three 4-inch pans. Coat lightly with flour, tapping out any excess.
Step 3
Combine the eggs, water, vanilla, and applesauce in your blender pitcher. Blend to combine.
Step 4
Sprinkle the flaxseeds on top and allow to sit for 10-15 minutes.
Step 5
Add the butter and blend until it is combined and the flaxseeds are fully ground.
Step 6
Add the oats and baking powder. Blend until the oats are fully incorporated.
Step 7
Divide the batter evenly between prepared cake pans. You may need to use a spoon or spatula to encourage the batter to the pan's edges. Jiggle and tap the pan to level the batter.
Step 8
Bake until a toothpick (or fork! I just use a fork) inserted in the center of the cake comes out clean. My 6" pans took about 18 minutes to bake the cake. It took about 25 minutes in the 4" pans because each layer was considerably thicker. Ovens and pans vary, so keep en eye on your cake and pull it when it's ready, not just because the clock said so.
Step 9
Allow the cakes to cool for about 5 minutes. Run a knife around the edge of the cakes to help them come free, then carefully turn them out onto a wire rack.
Step 10
Once the cake has fully cooled, you can "frost" it with whole milk Greek yogurt or the frosting of your choice. I allowed my Greek yogurt to drain in a colander in the fridge to remove any excess moisture so the cake wouldn't become soggy. Simply line a colander with cheesecloth or a Viva paper towel and let it sit for a an hour or so.
Step 11
Serve and watch your little one enjoy!