Heat 1 tbsp coconut oil and 1 tbsp unsalted butter in a large sauté pan over medium heat. Add your shredded coconut and stir to combine.
Cook for 3-5 minutes, stirring constantly, until coconut is deeply golden and caramelized. Remove from heat on a paper towel-lined baking sheet.
In a large bowl, combine 8 tbsp soft unsalted butter and 3 tbsp white sugar. Mix until pale, fluffy, and cohesive. Add 3/4 tsp kosher salt and stir.
Next add your 1 cup of AP flour and work into a fine crumb with your hands, a fork, or a pastry cutter. Add 1 egg yolk and work into your flour mixture until a dough comes together.
Gather dough into a disc and wrap tightly in plastic wrap. Chill for at least 30 minutes before rolling it out.
Remove dough from fridge and let warm for 10 minutes. Work with your hands into a 10" tart pan, spreading the dough evenly over the bottom and sides. Trim any excess with a knife.
Chill tart shell in the fridge again for 30 - 60 minutes. In the meantime, preheat oven to 350°F.
Remove tart shell from fridge and place in oven to bake for 30 minutes. Remove and let chill for at least 15 minutes in tart case. Carefully remove from metal case and place shell on a baking sheet.
Combine 1 cup white sugar and 1/2 cup water in a large saucepan over medium-high heat. Cook until the mixture bubbles, then turns a medium golden brown / amber color (about 10 minutes).
Remove from heat and carefully add 1/4 cup coconut milk and 2 tbsp coconut oil. Stir to combine and add 1 tsp flaky sea salt. Add 3/4 cup of your toasted coconut and stir to combine.
Pour coconut caramel sauce into the bottom of your tart shell. Spread evenly with an offset spatula and let cool at room temperature.
To make your pastry cream, heat 3/4 cup heavy cream, 1 cup coconut milk, 3/4 cup toasted coconut, and 1 1/2 tsp vanilla extract in a large sauté pan or sauce pan over medium heat for 5-10 minutes until bubbly.
Meanwhile, whisk together 3 egg yolks, 2 whole eggs, 1/2 cup + 2 tbsp white sugar, and 1 tsp cornstarch in a large heat-proof bowl.
Cook your coconut milk mixture for another 10 minutes to infuse flavor. Then, pour a ladleful into your egg mixture and whisk immediately. Add the rest of your hot liquid, gradually, until you have a thin, cohesive liquid.
Strain the mixture back into your hot pan, removing all coconut strands. Cook for 5-10 minutes, whisking constantly, until very thick. Remove from heat and add 2 tbsp unsalted butter, whisking to combine.
Pour your coconut pastry cream on top of the coconut caramel in your tart shell. Smooth with a spatula. Let cool for 30 minutes at room temperature, then cover with plastic wrap and chill for at least 1-2 hours until set.
When ready to serve, remove tart from fridge and uncover. In a large bowl or stand mixer, whisk together 1 1/2 cups heavy cream, 1 tbsp maple syrup, 1 tbsp white sugar, 1/2 tsp kosher salt, and 1/2 tsp vanilla extract until medium-stiff peaks form.
Spoon your whipped cream over your tart and smooth with a spatula. Top with the rest of your toasted coconut, slice, and serve.