I will only eat a skinny cake if it tastes like it is a fat cake.
Warm the coconut oil in microwave for up to 30 seconds; you want it softened or even melted (but not hot to the touch).
With mixer on low, slowly add a third of the dry ingredients into the applesauce mixture, alternating with the milk. Keep alternating until the dry ingredients and milk are gone.
Divide batter between two cake pans. Bake at 350 degrees for 22 to 26 minutes or until an inserted toothpick is removed clean. (Cooking times can vary depending on quality of ingredients and weather conditions.)
Beat butter and raspberry extract in large bowl with a handheld mixer until light and fluffy. Gradually add confectioners' sugar, beating well after each addition and scraping sides and bottom of bowl frequently.
Place one cooled layer of cake on cake stand. Cover with raspberry buttercream. (You can allow it to slightly spill out over sides)
If you need to store for longer, consider adding a 2-3 tablespoons of simple syrup over each cake to keep moist. (the cake will no longer be 'skinny')