Begin by peeling the cassava roots. Stand each root vertically and carefully remove the thick skin with a sharp knife. The flesh should be bright white with a faint ring of pink just beneath the surface.
Using the medium side of a grater, shred the peeled cassava finely. Measure out 4 cups of shredded cassava and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the shredded cassava, sugar, salt, and softened butter. Blend on medium speed until the mixture is cohesive.
Add the eggs, milk, coconut milk, shredded Parmesan cheese, and sweetened shredded coconut. Continue mixing until the batter is smooth and well incorporated.
Sprinkle in the baking powder and blend once more, ensuring it is evenly distributed throughout the batter.
Grease and flour a baking pan thoroughly. Pour the batter into the prepared pan, smoothing the top with a spatula.
Bake in a preheated oven at 350°F (175°C) for approximately 50 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.
Allow the cake to cool slightly before slicing. Serve warm or at room temperature for a rich, tropical dessert experience.