Preheat oven to 350 degrees F and prepare (spray or butter and flour) two 8-inch round cake pans.
Warm the coconut oil in microwave for up to 30 seconds; you want it softened or even melted (but not hot to the touch).
Pour coconut oil into stand mixer with paddle attachment.
Add in brown sugar, applesauce, yogurt and vanilla extract, and mix until combined.
In a separate bowl sift together flour, baking powder, baking soda, salt and cocoa powder.
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.
Remove bowl from stand mixer and fold in chocolate chips by hand.
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.)
Cool cakes in pan for 5 minutes and then transfer to wire rack.