I have a EG2800i - exact same engine as EB2800i
http://cdn.powerequipment.honda.com/pe/pdf/manuals/00X31Z43B011.pdf
Nothing in the owners manual about break in - and it would be a bad idea to let it run for hours with no load.
You want to get it hot and let it cool back down a few times -
This is how I broke mine in -
I bought a couple quarts of 10W30 conventional oil (SuperTec or whatever SN is cheap) Honda EG2800i does not come with oil -
It takes just under 20 ounces to fill -
I ran it for a few minutes to warm it up
Then 500 watts for 15 minutes
1,000 watts for 15 minutes
1,500 watts for 15 minutes
Then about 2,000 for 10 minutes
Then a few minutes at 1,000 and 500 and then let it idle for a few minutes then shut it down
Let it cool down - changed the oil
Then did the same thing again but went through two cycles so about 2 hours worth
Let it cool down and changed the oil
Then ran it hooked up to my breaker box with an interlock switch for 5 hours - power was out and it was really cold -
Then switched over to Honda 10W30 and changed it once per day - after I burned through 2 quarts of SuperTec breaking it in and 2 quarts of Honda 10W30 conventional I used Mobil1 10W30 full synthetic.