Slice pineapple into thick discs, trimming the top and bottom. Grill on high heat with a little bit of oil until deeply caramelized on both sides.
Let pineapple discs cool at room temperature. Meanwhile, heat butter and coconut oil in a large sauté pan over medium-high heat.
Once melted and bubbly, add your shredded coconut and toss to coat evenly in butter and oil. Cook, stirring constantly, until deep golden brown and toasted. Remove 1/3 to 1/2 cup of coconut for plating later and transfer to leftover container.
Pour in your coconut milk and heavy cream to deglaze the pan and stop cooking the toasted coconut. The mixture will bubble and thicken slightly, so stir it frequently until hot (3-5 minutes).
In a medium bowl, whisk together the egg yolks, sugar, and salt until pale and fluffy. Place a strainer over the top of the bowl and pour in your coconut cream mixture, straining out the toasted coconut. Save coconut for another recipe, or toast for extra garnish.
Once your mixture is strained, wipe out your coconut pan with a paper towel and pour the mixture back into the clean pan. Heat over medium-high heat and whisk constantly for 5-10 minutes until thickened (mixture should coat the back of a spoon and have a custard consistency).
Once thickened, remove from heat and let cool to room temperature. Meanwhile, cut up your cooled caramelized pineapple. Remove the core from the center with a cookie cutter or knife and remove outer hard skin. Place in the freezer to firm for about 10-30 minutes. It should be solid and cold but not fully frozen.
In a large blender, combine your coconut anglaise, lime juice, and cold caramelized pineapple. Blend until silky and totally combined, for about 2-3 minutes. Stop and scrape sides if needed.
Strain your anglaise into a clean bowl, removing any coarse pieces of pineapple. Cover with plastic wrap and chill in the fridge for at least 2 hours, or up to overnight.
When ready to churn, pour your anglaise into a frozen ice cream machine and churn for 15 - 25 minutes. Be careful not to over-churn (the water content in the pineapple makes this more likely than other ice cream recipes).
When the consistency is similar to a thick but pliable ice cream, remove from ice cream machine and spread into a metal dish. Cover and freeze for at least 30 minutes to firm.
When ready to serve, place 1-2 tbsp toasted coconut on your plate in a ring mold. Then, scoop a ball of ice cream and place on top of the coconut. Garnish with a pineapple leaf.