Make the cake.  Preheat oven to 350 degrees F/325 degrees F convection.  Oil two 8 or 9 inch cake pans and line the bottom with parchment.

In a large bowl, stir together the sugar, oils, and vanilla until fully combined.  Beat in the eggs and yolks one at a time until combined.  Stir in half the flour, followed by half the milk.  Stir in the remaining flour, tapioca, baking powder, salt, and turmeric.  Finish the batter with the remaining milk.

Divide between the prepared pans and bake for 25-30 minutes until golden brown and a toothpick inserted in the center comes out clean or with a few moist crumbs.  Cool completely in the pans.

When ready to assemble the cake, make the frosting.  In a jar of a high speed blender, place the cashews, syrup, vanilla, espresso, carob or cocoa, and 1/3 cup milk.  Blend on high, using the tamper if applicable, until completely smooth and emulsified, scraping down at least once to ensure complete blending.  If the frosting is too thick, add more milk until it is the proper consistency.

Place one cake on the cake stand or serving platter of your choosing.  Top with about ¾ cup of frosting, smoothing to the edges.  Place the remaining cake on top, and then heap frosting over the cake.  smooth frosting toward the edges and down the sides until the cake is fully frosted.

Serve immediately or store in an airtight container in the refrigerator for up to 4 days.