Mold spores are everywhere. Always. They were in your soil when you first got your EarthBox, and they will be in your soil when the white stuff goes away. Just chill and move on. Just a harmless saprophytic fungus. If the mycelium offends you, just scrape it off or dig it in. It's just indicating that your soil was left overly moist, and it's happily feeding on the organic matter in it.

Dig it back in. If it bothers you, drop a heaping handful of ordinary corn meal over the surface and moisten it slightly. Corn meal seems to have a restorative effect.

Did Dave's instructions include putting the cover back on? I wonder if Dave has done side by side by side comparison of reusing the Earthbox without his treatment, with the treatment, and fresh/new to see how the second year veggies grow.

It doesn't bother me. I just didn't want it to be something that will affect the growth of my plants this season. I can't seem to find the post where Dave/digdirt2 explained what he does with his Earthbox renewals, but I know I didn't dream it.

I think I will experiment - do some with Dave's method and some just leaving all soil in place like Tony does (removing old plant root ball only) and adding new fertilizer.