Preheat the oven to 350°F

Put the ½ cup sugar and the canola oil in the bowl of a standing mixer fitted with the paddle attachment, and paddle until creamed together, approximately 2 minutes. Add the egg and mix well.

Sift the salt, cinnamon, baking powder, and flour together in a bowl. Add this to the egg mixture and mix well, scraping down the sides of the bowl with a rubber spatula. Add the shredded pineapple, carrots; and coconut, and mix well.

Spray the mold (see headnote) with nonstick cooking spray, and pour in the batter; it should reach two-thirds of the way up its sides. Bake for 15 minutes. Then rotate the pan and bake until the cake is browned on top or until a paring knife inserted in the center comes out clean, 7 to 10 minutes. Remove the cake from the oven and set it aside to cool.

Meanwhile, mix together the diced pineapple, lime zest and juice, and remaining 2 tablespoons sugar.

When the cake has cooled completely, unmold the cake onto a cutting board, and cut it into thick slices. Divide the slices among individual plates, and serve with some of the diced pineapple alongside. Add a topping of coconut sorbet, if desired.