Combine 24 oz cream cheese, 12 oz granulated sugar and ⅛ teaspoon table salt in a mixing bowl. Mix on medium speed to combine the ingredients, scraping the bowl and beaters often to avoid lumps.
With the mixer running on low speed add 12 oz canned coconut cream, 1 oz rum and 1 teaspoon vanilla extract. Scrape the bowl. In a small bowl, whisk 5 large eggs and add them in two stages, scraping well after each addition. Mix just until the eggs are combined, do not over mix.
Pour the batter into the cake pan. Set the cake pan into a larger pan. Set the pan onto the middle rack of the oven and pour water into the larger pan to come at least ½ way up the side of the cake pan.
Bake until the cake softly jiggles as a mass when the pan is shaken, about 1½ hours. (see note)
Remove from the oven and cool for 10 minutes. Run a thin sharp knife that has been moistened with warm water around the sides of the cake to release it from the pan (this will prevent the cake from cracking while it cools). Refrigerate at least 6 hours or overnight.
If you used a springform pan run a knife around the sides of the cake and release the sides of the pan. If you used a regular cake pan, set the cold cake pan into a bowl of very hot water for 20-30 seconds to release the sides. Run a warm knife around the sides of the cake. Place a plate or cardboard cake circle covered with plastic wrap on top of the cake pan. Immediately flip the cake over and remove the pan and the parchment circle. (See Note) Flip the cake over onto a serving plate.
Whip 8 oz heavy cream with 1 oz confectioner sugar, 1 tablespoon rum and 1 teaspoon vanilla extract to full peak. Spread the cream in a swirling pattern over the top of the cake. Sprinkle with ½ cup sweetened coconut flakes.