Preheat the oven to 350°F. Line two 6-inch cake pans with parchment paper.
To make the batter: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, zucchini, and brown sugar. Mix on low until combined and there are no butter chunks.
Add the coconut milk, flour, coconut flour, coconut, baking powder, sea salt, and cinnamon, mix on low until combined.
Transfer to the prepared cake pans, about 15 ounces each.
Bake for 30 to 35 minutes or until a toothpicks inserted in the center comes out clean. Allow to cool completely in the pans.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, powdered sugar, and strawberries. Mix on low until combined and then speed mixer up to high and mix for 2 to 3 minutes, or until light and fluffy.
Transfer the frosting to a piping bag with Ateco tip #827. Place the first cake layer on a plate and pipe a spiral of frosting starting at the outer edge and working your way into the middle. Place the second cake layer on top and repeat this process. Top with sliced strawberries.
Store in an airtight container in the fridge for up to 3 days.