Place the graham crackers and coconut into a food processor and pulse until they form a very fine crumb. Pour into a bowl and add the baking powder and mix together.
Place the butter in a large bowl and beat with an electric mixer until light and smooth. With the mixer still on, slowly add the sugar. Keep whipping for 5 minutes until it is light and fluffy.
Add the egg yolks one at a time, mixing well after each addition. Then add the vanilla extract and mix well.
Add the graham cracker mixture in 3 additions, alternating with milk (graham crackers > milk > graham crackers > milk > graham crackers). Mix until fully combined, then add the chocolate chips and mix again.
Place the egg whites in a separate bowl, and beat with an electric mixer until they become frothy. Add the cream of tartar and continue whipping until you reach stiff peaks. Place ¼ of the egg whites into the graham cracker batter and gently mix together. Then add the remaining egg whites and gently fold into the batter, keeping it as airy as possible.
Pour the batter into 2 buttered 9-inch round cake pans. Bake at 350F for 25-30 minutes until fully cooked.
Allow the cakes to cool in the pan for 10 minutes, then turn out onto a cooling rack and completely cool.