Preheat the oven to 350° on the Convection Roast setting, if available. Otherwise 375° “Bake” is okay too.
Cut the cauliflower into 2-inch flower-ettes and spread in an even layer on a large baking sheet. Roast/Bake for 30 minutes or until slightly browned and tender.
Meanwhile: Prepare lemongrass by removing any tough outer layers and cutting into a 4 to 5-in length from the bottom/thick end. Slice each piece in half lengthwise, then slice lengthwise several more times resulting in thin strips. Now slice crosswise to create a fine mince.
In a 3-quart saucepan, melt the coconut oil over medium heat. Add the lemongrass, shallot, and ginger; and cook until softened. Add the broth and bring to a low boil. Cover with a tight-fitting lid and simmer at the lowest possible heat whilst the cauliflower finishes roasting.
Transfer the roasted cauliflower into a blender, and add enough of the broth, about 1 cup, to facilitate blending. Add the remaining broth, then blend until smooth. Be careful with the hot liquid! [Alternatively, you can use an immersion blender. For this method, add all of the roasted cauliflower to the simmering broth. Turn off the heat, then blend with the immersion blender until smooth. This method will not result in as smooth a texture, but still delicious.]
Finally, add the can of coconut milk and stir to combine. Add salt and white pepper to taste. Thin if needed with water. Bring to a low boil. Adjust seasonings to taste then serve hot.