The POD is after the Norwegian King Harold Hardrada (1015 - 1066) joined the Varangian Guard.
He left the Varangian Guard earlier than in our time. He came to the famous House of Wisdom library (source: The Islamic World, first episode of What the Ancients Did for Us). He would have at least looked at the Roman siege machines, like the ballista and "half torsion catapult", the plate armour or even the tortoise formation. He may have been interested in aqueducts or the theory of clean war camps and maybe even toilets. If so, all battles he took command of as King may have improved in his favour. Since more of his soldiers survived than in our time, history inevitably changed because that would have enabled a better fit of men and jobs. He may have even brought back the number zero.
When he returned to Norway, he brought relevant books with him and that triggered better fortress techniques (because the imbalance by his new knowledge triggered an arms race).
If stories of where he found those books survived his death, more people may have heard of the Islamic translated knowledge and that may have triggered an earlier translation movement and earlier Renaissance.
The Battle of Stamford Bridge would perhaps have resulted in a minuscule amount of more casualties for the Saxons, because of the more hygienic army than in our time if he had read books on army hygiene. Some more Normans thus survived the Battle of Hastings because of that. Another Norman ruled differently than the Norman that ruled the same domain in our history. For example, a war may have been different, because of the child-raising styles of those Normans were different. Their sons lived better lives than in our time. They may have been less paranoid and indirectly lost more battles than in OTL. Or they may have been less insecure and thus had fewer rebellions than in OTL.
He died in the Battle of Stamford Bridge that proceeded the Battle of Hastings, just as in our history.