Grease a 9" x 2" (22 x 5 cm) round cake pan thoroughly on the sides and bottom. Line the bottom with parchment paper and grease the top of the parchment paper. Be sure to get the corners good! Arrange an oven rack in the center of the oven. Preheat the oven to 350F (180C).
Place the nuts on a small sheet pan and put them in the oven while the oven is preheating. Toast the nuts for about 10-15 minutes, or until the nuts are fragrant and starting to turn slightly darker. Chop fine when cool. Scoop out 1/4 C (25g) for sprinkling on the top of the finished cake. Set aside.
In a medium mixing bowl, add the flour, corn starch, salt, baking powder, baking soda, cinnamon, and nutmeg. Whisk to combine. Set aside.
In a large mixing bowl, add the brown sugar and cane sugar, and whisk in the oil until ingredients are combined, about 30 seconds. Add the eggs and vanilla. Whisk until the ingredients are emulsified, about 20 seconds. Add the pineapple to the egg mixture and whisk until the pineapple is evenly distributed. Add the dry ingredients to the wet ingredients. Using a silicone spatula, gently mix until no flour streaks remain. If using coconut oil, the batter will start to stiffen at this point because the coconut oil is cooling (solidifying). Working quickly, fold in the shredded carrots and nuts. If using canola oil, the batter should be thick but loose and almost pourable. For coconut oil, the batter should be stiff and thick.
Transfer the cake batter to the cake pan and using an offset spatula, and smooth the batter into an even layer. If using coconut oil, spread the batter while pressing it into the pan. Tap the pan on the counter to disperse any air pockets.
Bake the cake for 30-40 minutes. The cake is ready when it's golden, a toothpick poked in the center comes out clean, the cake slightly springs back under gentle pressure at center, and the edges of the cake are just starting to pull away from the sides of the pan. Allow cake to cool in the pan for 20 minutes on a cooling wrack. Turn cake out on to a plate or cutting board to release. Give it a gentle tap if needed. If it doesn't budge, ease the edges with a pairing knife by running the knife around the sides of the cake. Then flip back over on to cooling rack, so that the top is showing. Cool completely before icing (about 2 hours).