Using an electric stand mixer fitted with the paddle attachment, beat the butter, cream cheese, sugar, and curry paste in the mixer bowl until smooth and fluffy. Mix in the coconut extract. Use immediately or transfer the frosting to a covered container and refrigerate for up to 2 days; allow the frosting to come to room temperature before using it.
Cook the carrots in a large saucepan of boiling water for about 25 minutes, or until they are very tender. Drain the water and puree the carrots in a blender until smooth. Measure out 2 cups of carrot puree to use in the cakes; reserve any remaining puree for another use.
Preheat the oven to 375⁰F. Butter and flour twelve 3-inch-diameter ring cake molds with 2-inch-high sides.
Stir together the flour, cinnamon, baking powder, and salt in a medium bowl. Using an electric stand mixer fitted with a whip attachment, beat the eggs with the sugar on high speed for 3 minutes, then, with the mixer still running, slowly stream the oil into the egg and sugar mixture. Turn off the mixer and add the carrot puree, then mix on medium speed until fully incorporated. Turn off the mixer and add the dry ingredients, then mix on low speed until fully incorporated, about 30 seconds. Do not over mix. Stir in the walnuts.
Spoon the batter into prepared cake molds, dividing equally. Bake for 25 minutes, or until a toothpick inserted into the center of a cake comes out with some crumbs attached.
Stir together all the ingredients in a medium bowl. Freeze in an ice cream maker following the instructions for your specific ice cream machine.
Press the sorbet into a plastic container, and cover with plastic wrap pressed directly on the surface of the sorbet. Freeze until scoopable. If you’re freezing the sorbet overnight, allow it to soften slightly before scooping it.
Combine all the ingredients in a small saucepan and bring to a boil over high heat. Remove the saucepan from the heat and allow the syrup to cool. Cover and refrigerate for a few months.
Unmold the warm cakes from the pans. Place 1 warm cake on each plate. Spoon some frosting onto the plates. Spoon 1 scoop of mango sorbet onto each pate. Divide the kaffir lime oil into small ramekins and serve them alongside the cakes.