In the bowl of a stand mixer, combine the sugar and egg yolks. Using the whisk attachment, beat on medium-high speed until the mixture is light and fluffy, about 5 minutes. Be sure to stop the mixer every couple of minutes to scrape down the sides of the bowl.
While the eggs and sugar are mixing, combine the coconut milk and coconut cream in a saucepan. Heat on low until the liquid begins to scald and you see steam rising, then remove the pan from heat.
Add the flour and cornstarch to the egg mixture and whisk until well combined, stopping the mixer as needed to scrape down the sides of the bowl.
With the mixer running on low speed, slowly add a small amount of the hot coconut milk to the egg mixture to temper the eggs. Mix well, then gradually add the remaining coconut milk, continuing to mix until fully incorporated.
Transfer the entire mixture back to the saucepan. Heat over medium-low heat, whisking frequently, until the pudding thickens, about 5-10 minutes. Stir in the coconut rum (or vanilla if substituting).
For toasted coconut topping, add the sweetened coconut flakes to a large pan and cook over low heat, stirring frequently, until golden brown. Once the coconut starts to brown, stir continuously to prevent burning.
Serve the pudding warm or cold, topped with toasted coconut flakes. You can also mix the toasted coconut directly into the pudding before serving if preferred.