Lightly grease a 9x13-inch baking pan. Cut two long strips of parchment paper and lay them across the pan in opposite directions, overlapping in the center and extending up the sides. These strips act as handles and can be removed before adding the soak.
Preheat the oven to 350°F, which is 175°C. Open the canned coconut milk and pour it into a bowl. Whisk until smooth. You will need about 1 1/2 cans total for the batter, soak, and frosting.
In a small bowl, whisk together the flour, baking powder, baking soda, and salt. Set this dry mixture aside.
In a large mixing bowl, beat the butter for about 30 seconds. Add the sugar and beat for another 4 to 5 minutes until the mixture is light and fluffy.
Add the neutral oil and beat for one minute to combine.
Add the eggs one at a time, mixing well after each addition. Along with the final egg, add the vanilla extract and coconut extract.
Add the sour cream and stir until combined.
Add one third of the dry ingredients and mix on low. Then add half of the coconut milk and mix. Follow with another third of the dry ingredients, stirring just until incorporated.
Pour in the remaining coconut milk and mix. Add the remaining flour mixture and stir gently. Fold in the sweetened shredded coconut.
Pour the batter into the prepared pan and spread it evenly. Bake for 32 to 38 minutes. The cake is done when the center springs back lightly and a toothpick comes out with just a few moist crumbs.
Make the coconut milk soak by whisking the sweetened condensed milk and coconut milk together until smooth.
Once the cake has cooled for about 30 minutes, poke holes all over the surface with a skewer or fork. If you used the parchment paper method, gently pull the strips out from underneath the cake before adding the soak.
Slowly pour the soak evenly over the cake. It may look like a lot at first, so give it a moment to absorb before adding more. Use a pastry brush to spread the soak evenly across the surface.
Cover the cake with plastic wrap and refrigerate for at least a few hours, preferably overnight. The cake can be frosted once most of the syrup has soaked in.
To make the coconut cloud frosting, beat the butter for 30 seconds. Add the cream cheese and beat for another minute until smooth.
Add the powdered sugar and beat until incorporated. Then add the coconut milk, vanilla extract, and coconut extract. Mix until combined and set aside.
In a separate bowl, whip the cold heavy cream to stiff peaks using an electric mixer on medium-high speed. Stop as soon as the peaks are stiff but still smooth. Do not over whip.
Fold half of the whipped cream into the cream cheese mixture. Add the remaining whipped cream and fold until light, fluffy, and fully combined. The frosting should feel airy and mousse-like while still holding its shape.
Spread the frosting over the chilled cake. Top generously with shredded coconut. Chill for at least 30 minutes before slicing.