Pour the entire can of unsweetened coconut cream into a small mixing bowl and whisk to re-combine.
In a small bowl, whisk together cornstarch, flour, sugar, and eggs until fully combined.
In a saucepan, combine coconut cream and milk, then add shredded coconut and heat until frothy.
Temper the egg mixture by adding a tablespoon of the hot mixture to it, whisking quickly, then combine with the saucepan.
Cook the mixture over medium-low heat until thick and custard-like, then add coconut oil, butter, and vanilla extract.
Chill the coconut pastry cream until cold.
Preheat oven to 350°F and prepare a 9x9 inch cake pan.
Mix yogurt, coconut oil, and sugar in a large bowl, then add vanilla and eggs one at a time.
Add baking soda, salt, and flour, mixing until just combined.
Transfer batter to the prepared pan and bake for 25-30 minutes.
Allow the cake to cool, then chill in the fridge.
Whip heavy cream, vanilla, and powdered sugar until stiff peaks form.
Spread coconut pastry cream on the cooled cake, top with whipped cream, and chill before serving.