Cellphones can hard boil an egg?

We tried the experiment in class. One student had claimed that he had tried it at home so I let him set the whole thing up. I offered him the chance to smash the egg against his forehead after the hour was up. If the experiment didn’t work, he would look pretty stupid. At first he agreed but later he changed his mind.
At the end of the hour the egg was room temperature as expected but I still had a handful of students who thought we would at least get a soft cooked egg.
The egg was perfectly raw.
It was amazing the number of students who thought that popcorn would be a better choice than an egg. They had seen a few too many Youtube videos. I showed them a video that showed how the hoax was perpetrated.
I also talked about how cellphones are not walkie talkies, they don’t talk to each other but through a cellphone tower.
A good question came up: Since cell phone towers communicate via microwaves, can I hard cook an egg if I climb a cell phone tower?

I don’t have any personal experience on this one, but I do know people that have done repair work on towers of different kinds (Cell and TV, I believe are the only two I know people who have done work on). They were amateur radio operators that either did the TV tower stuff as a main job or had repeaters on TV towers… In either case they said that before they climbed up the antennas WERE TURNED OFF. Their reasoning… They weren’t big fans of cancer.

Looks to me like cooking an egg with cell phone signals, even with a cell phone tower is too difficult to bother:

Mobile Telephony and Health Exposures from Base Stations