For the Pineapple: Peel the pineapple and leave whole. In a saute pan, melt the butter and add the brown sugar and vanilla beans. Cook to caramelize the sugar; then place the pineapple in and cook on all sides until brown. Add some water to the pan and continue cooking, turning the pineapple with tongs and basting occasionally until cooked through to the core. It may take 1 hour or more. Chill, then slice thin on an electric slicer set on #12 or slice thinly by hand.
For the Coconut Cilantro Dressing: Whisk the ingredients together and chill.
For the Macadamia Nut Brittle: In a saucepan, boil the sugar and water together to make a caramel. Test the color of the caramel on a white plate--you're looking for a topaz color. Turn off the heat and stir in the butter with a wooden spoon then stir in the nuts. Pour onto a silicone baking mat and let cool. Chop and keep in an airtight container.
For the Crystallized Cilantro Leaves: Place egg white in a small bowl and whisk it slightly to break it up a bit. Dip the individual leaves in the egg white and wipe them off on the edge of the bowl to remove any excess. Dip into granulated sugar on both sides. Let dry.
For the Coconut Butter Cookies: In a mixer with a paddle attachment, whip the butter until very light and fluffy, warming the bottom of the bowl with a torch if needed. Add the sugar and continue whipping; then add the rum and vanilla and mix. Toss together the coconut, flour, and salt; then add to the butter mixture and mix until blended.
Butter a small sheet pan and line it with plastic all the way up the sides. Spread the dough evenly into the pan, cover it with plastic and freeze. Cut into 2-inch strips and roll in flour. Wrap and freeze or cut into 1/8-inch bars and place on parchment lined sheet pan. Bake in a preheated 250 degree F. oven until crisp but barely any color, about 10 minutes. Let cool.
To make the Coconut Strips: Heat a whole coconut over a gas flame to slightly char all sides. Wrap it in a tea towel and whack it on the floor to break it open. Carefully pry the meat from the shell in as whole pieces as possible. With a vegetable peeler, peel off thin strips of the fresh coconut meat to end up with curves of fresh coconut. Store in simple syrup, chilled to cover.
To serve the dish: Place 5 to 7 slices of pineapple on a plate in a flower pattern, with 1 in the center, surrounded by the others. Brush the surface of all the slices with the coconut cilantro dressing. Cover the plate with plastic wrap and warm it in the microwave oven for about 1 minute. Remove the plastic wrap and sprinkle with freshly ground black pepper and macadamia nut brittle.
Place a quenelle of lime sherbet in the middle and drape coconut shavings in an X over the sherbet. Place 2 crystallized cilantro leaves on top. Serve with a side of coconut shortbread cookies using colorful origami paper under the cookies and stacking them in a criss-cross tower, like bruscetta with the carpaccio.