Make the crust first. In a mixing bowl or in the bowl of a food processor, mix together the toasted coconut, ground almonds and melted butter. Press mixture into the bottom of a 9-inch springform pan.
To make the filling, in a large mixing bowl beat the softened cream cheese with ½ cup sugar, and amaretto or almond extract. Add the three whole eggs all at once and beat on low just until combined. Scrape filling into the pan and over the crust, then set the cake on a rimmed baking sheet.
Bake at 350F for 40 minutes. (Cheesecake will not be completely done.) Sprinkle with the remaining ⅔ cup toasted coconut. This is a partial bake. You will remove the cake after 40 minutes and add the topping.
In the bowl of a stand mixer using the whisk attachment, beat the egg whites with the cream of tartar until soft peaks form. With mixer going, gradually add the sugar beat until peaks become stiff. Beat in the vanilla.
Spread mixture over the partially baked cheesecake, sprinkle with a little more coconut (⅓ cup) and bake for another 15 minutes or until lightly browned.
Let cool on wire rack for 15 minutes. Loosen the sides from the pan but don't remove ring yet. Let cool for 30 more minutes, then remove cheesecake pan ring. Let cool for another hour, then chill for at least 4 hours before serving.
Just before serving, heat chocolate and shortening in a small microwave-proof bowl or custard cup stirring every 30 seconds until smooth. Fling little bits of chocolate over cold cheesecake and let set.