Potatoes Reloaded?

So..... last years 1st attempt at growing potatoes was a bust. Built a wire cage everything looked good but the straw I used to top up filled with black mold and I never peeked underneath. Shoots got to be about 36" high. I was getting ready to level what was left to make way for herbs but noticed some new potato shoots coming up and was tempted to hill up with soil. Can I just try again without disturbing the pile? I know little about potatoes.
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Oh, and 1 more thing. I moved a little corner of the straw... boy is it loaded with worms.
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