Preheat the oven to 350°F. Line three 6-inch cake pans with parchment paper.
To make the batter: Chop the strawberries into small pieces.
In the bowl of a stand mixer fitted with the paddle attachment, add the strawberries, cane sugar, grated carrots, canola oil, coconut milk, and vanilla extract. Mix on low until combined.
Add the flour, cornstarch, baking powder, sea salt, and cinnamon in that order. Mix on low until combined. Transfer to the prepared cake pans, about 269 grams each, and spread evenly.
Bake for 20 minutes or until a wooden pick inserted in the center comes out clean. Allow to cool completely in the cake pans.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the vegetable shortening, powdered sugar, coconut milk, vanilla extract, and sea salt. Mix on low to combine, then increase speed to high and mix for 1 minute or until light and fluffy. Scrape down the sides of the bowl and mix again until light and fluffy. Transfer to a piping bag with Ateco tip #827.
Place the first cake layer on a cake stand or plate. Pipe a spiral, starting at the outer edge and working your way in, to cover the cake layer with frosting completely. Top with the second cake layer, repeat this process with the third layer. Then spiral again on the top to finish the cake. Top with strawberry slices (optional).
Store in a cake dome in the fridge for up to 3 days.