Preheat the oven to 325°. Spray six 6-ounce ramekins with cooking spray. Lightly dust the ramekins with granulated sugar, tapping out the excess.
Peel the mangoes. Cut 1 of the mangoes off the central pit in neat slices and set aside. Coarsely chop the 2 remaining mangoes. In a food processor, combine the chopped mangoes with 1 teaspoon of the sugar and puree until smooth. Strain the puree through a fine sieve set over a small bowl.
In a large bowl, beat the cream cheese with the remaining 1/3 cup sugar until creamy. Add the eggs, 1 at a time, and beat until smooth. Stir in the mango puree, lemon juice and vanilla. Pour the mixture into the prepared ramekins and set them in a roasting pan. Pour enough water into the pan to reach halfway up the sides of the ramekins.
Bake the cheesecakes for about 30 minutes, or until firm around the edges and slightly soft in the middle. Remove the ramekins from the water bath and let cool. Cover the cheesecakes with plastic wrap and refrigerate for at least 6 hours or for up to 2 days.
In a food processor, combine the macadamias with the all-purpose flour, rice flour, granulated sugar, brown sugar and salt; pulse until the nuts are finely chopped. Add the butter and pulse until the dough resembles coarse meal. With the machine on, add the milk and vanilla, and process until the dough just comes together.
Roll out the dough between 2 sheets of wax paper to form a 1/4-inch-thick rectangle. Refrigerate until firm, at least 1 hour or overnight.
Preheat the oven to 325°. Peel off the top layer of wax paper and use a 2 3/4-inch round biscuit cutter to stamp out 6 rounds. Set the rounds on a baking sheet lined with parchment paper and bake for 12 to 15 minutes, or until the edges are light brown and the centers are firm. Transfer the rounds to wire racks to cool completely.
Just before serving, tilt the ramekins over the sink to drain off any liquid. Top each cheesecake with a shortbread round and invert them onto dessert plates. Garnish with the mango slices. Serve with the Coconut-Tapioca Sauce.