Preheat the oven to 350 degrees F (180 degrees C).
For the coconut filling: Pop the coconut in the oven and bake until it starts to crack, about 1 hour. Let cool and remove the outer shell. Reserve the coconut milk for another use, such as Adobo Pork Shanks with Fried Rice. Using a food processor, reduce the flesh to a fine powder.
Spread 2 cups coconut on a parchment-lined baking sheet. Toast in the oven until golden brown, about 10 minutes. Let cool.
For the lime shortbread crust: Pulse the all-purpose flour, confectioners' sugar and lime zest in a food processor to combine. Add the butter and pulse until coarse crumbs form. Add the egg yolks and process just until the dough forms a ball. Flatten the dough into a disk, wrap in plastic wrap and refrigerate for 30 minutes.
Roll out the dough on a floured surface and fit into an 8- to 9-inch (20 to 23 centimeter) tart pan with a removable bottom. You can use your fingertips to evenly press the dough onto the bottom and up the sides of the pan.
Finish the coconut filling: Beat the almond flour, butter, confectioners' sugar and toasted coconut with a mixer until creamy. Add the eggs and beat until pale and creamy, 2 to 3 minutes. Pour the coconut filling into the pie shell. Refrigerate for 1 hour. (This will help prevent the crust from shrinking while it bakes.)
Position an oven rack in the center of the oven and preheat to 425 degrees F (220 degrees C).
Bake the tart until golden brown, about 30 minutes. Let cool.
For the pineapple jam: Bring the sugar and 1 cup (250ml) water to a simmer in a saucepan over high heat, stirring until the sugar is dissolved. Reduce the heat to low, add the pineapple and cardamom seeds and cook for about 30 minutes, stirring occasionally.
Spread the pineapple jam over the cooled tart. Garnish with coconut shavings.