Potato towers: First layer
I topped them off with a few inches of compost and rice straw from old straw wattles (great because it won't sprout).
And that's it! As the vines grew taller, I simply topped them off with more rice straw for the tubers to grow in.
That's right: After that first topping off with compost and straw, I added no more soil.
See rice wattles used as raised beds