Preheat the oven to 350°F.

Grease two 5 or 6 inch cake pans or three 4 inch pans with butter or oil, then dust lightly with oat flour or gluten free flour, tapping out any excess.

Add the applesauce, eggs, and vanilla bean paste to a blender and blend until smooth.

Sprinkle the whole flaxseeds over the blended mixture and let sit for 10 to 15 minutes to hydrate and thicken slightly.

Add the softened butter slices to the blender and blend until the mixture looks creamy and no visible flaxseed pieces remain.

Add the oats and baking powder to the blender and blend until the oats are fully broken down and the batter is smooth and thick, scraping down the sides as needed.

Divide the batter evenly among the prepared pans and smooth the tops with a spatula; tap the pans gently on the counter to release any large air bubbles.

Place the pans in the oven and bake for about 20 to 25 minutes, or until the tops look set, the edges are very lightly golden, and a toothpick inserted in the center comes out mostly clean with a few moist crumbs.

Let the cakes cool in the pans for 5 minutes, then run a thin knife around the edges and carefully turn the cakes out onto a wire rack.

Cool the cake layers completely on the rack before frosting.

Once cool, place one cake layer on a serving plate and spread a thin layer of Greek yogurt over the top.

Stack the second layer, if using, and spread Greek yogurt over the top and sides to lightly frost the cake.

Chill the frosted cake until ready to serve, then let your little one enjoy their smash cake.