I had a coworker at my last job who did this, as part of her breakfast every morning.
Wish I had a recipe for you.

Shouldn't you just be able to bring your water to a boil and then drop the egg in there, sit for 10 minutes covered and bam boiled egg?

Where's the fun in that?

No fun whatsoever.

I steam my "hard boiled" eggs, but in a steamer basket and not with my steam wand. Steam "boiled" eggs are quite easy to heat to the level of cook we like.

The scrambled eggs with a steam wand looked quite interesting, although I don't think I'll try to replicate that!

Success!

Intrepid gave me the idea to cover the pitcher.

This time I did this:

1. Used the larger, 20oz pitcher instead of the 14oz. Under the grouphead, egg inside, and filled it up with water. Good for replenishing the brew boiler water.

2. Set aside covered with a saucer.

3. By the time I heated up the frozen gyro bread, 10 minutes, it was still hot.

4. Took it to the steaming wand and brought to almost a boil, placed aside and went to prepare the sandwich/gyro. When it was ready for the egg to go in, I took it out of the pitcher and it was a hard boiled egg!

I could probably skip the steaming to a boil step.

Woohoo!