Preheat oven to 350°F (175°C). Grease and flour two 9-inch cake pans.
Combine golden flaxseed meal and warm water in a small bowl. Set aside for 5 minutes to thicken.
In a large bowl, sift together flour, evaporated cane juice, baking soda, baking powder, arrowroot, and sea salt.
In a separate bowl, whisk together vanilla soy milk, safflower oil, vanilla bean paste, and white rice vinegar.
In another large bowl, beat the palm shortening, powdered sugar, agave nectar, and basil-infused oil until light and fluffy.
Add the flaxseed mixture to the shortening mixture and beat to combine.
Alternately add the dry ingredients and wet milk mixture to the shortening mixture, beginning and ending with dry ingredients; mix until smooth and well blended.
Divide batter evenly between prepared pans and bake for 32-35 minutes, or until a toothpick inserted in the center comes out clean.
Let cakes cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
For the strawberry-basil icing, beat together the remaining palm shortening, sifted powdered sugar, strawberry puree, and basil-infused oil until smooth and creamy. Adjust sweetness or texture by adding more sugar or puree as needed.
To make the ganache, heat coconut milk until just simmering, then pour over chopped dairy-free semisweet chocolate. Let sit for 2 minutes, then stir gently until smooth and glossy.
Place one cake layer on a serving plate, spread a layer of strawberry-basil icing over it, then top with the second cake layer and coat the entire cake with the remaining icing.
Use a spoon or piping bag to drip the chocolate ganache along the edges of the cake, allowing it to drip down the sides.
Refrigerate for at least 30 minutes to set the ganache before serving.