I'm no more than an educated shade-tree mechanic, but I can share with you the information provided to me by my ASE certified, UTI graduate friend.
For some motors, just starting it and letting it run breaks it in. Simple as that. Of course, everything is new and needs to settle, but that will all happen without any harm being done.
Mostly, the extensive break-in periods that most think are necessary, come from old-school folks who, back in the day, needed to spend a lot of time/effort breaking in their motors (i.e. hot-rodders breaking in solid flat tappet motors.) Nowadays, it's never a bad idea to take some precautions, but then again, may not be necessary.
My opinion is that you should take it easy, but not necessarily on RPM. Sure, don't wind it way up for a while, but think about throttle position in relation to RPM. I would rather have the motor spinning 6k rpm, vice 2k rpm and a wider throttle opening. Find a middle-of-the-road approach, and let it breathe, but don't thrash it. This is where you will be at maximum efficiency. And if you believe that the way you break it in is how it will perform, how can you beat that? Power and fuel mileage both come from efficiency, after all.