The England captain still recalls his early meetings with the prickly young opponent and team-mate whose vocabulary was apparently confined to a series of obscene grunts.
A decade on, with evergreen Anderson just seven short of Sir Ian Botham’s all-time England Test wicket-taking record, it is the 32-year-old’s ability to make the ball ‘talk’ which leaves Cook in awe.
Anderson is still prone to pushing the boundaries in verbal exchanges, his aggressive on-pitch persona reportedly a pre-requisite for channelling optimum performance from his swing and seam repertoire.
But as Cook prepares to deploy Anderson again in the fifth Investec Test against India at The Oval today – in his prolific pace partnership with Stuart Broad, fit despite a broken nose – the captain’s appraisal tells it pretty straight too.
Anderson’s mastery and disguise of swing places him above even South Africa’s Dale Steyn among his global contemporaries, in Cook’s estimation.
Should he underline the point by equalling or even passing Botham’s 383 Test wickets as England seek to turn a 2-1 lead into a series victory over India, Anderson’s status as England’s greatest will be no mere matter of opinion but statistical fact.
“It’s an amazing achievement,” said Cook.
“If he does it in this game, I think it’ll mean England are in a very strong position.
“He’s the most skilful bowler in the world.”
Anderson exemplified not just that but also an admirable tenacity when he defied the discomfort of an untimely virus to cut through India’s top order en route to victory in his home Test at Old Trafford last week.
“You saw his guts and determination, when he was bowling when he wasn’t very well,” continued Cook. “That was extraordinary. That pretty much tells me, tells everyone, what a bloke he is.”
Anderson’s continued quest for improvement is another reason Cook rates him so highly.
“There have been some very good bowlers I’ve played with, but for pure out-and-out skill and bowling ability, there is no doubt (he is the best).
“No disrespect to Dale Steyn, but the way Jimmy can swing the ball both ways, I don’t think Dale can do that quite as well as Jimmy.
“What amazes me is how he keeps trying to improve his bowling ... you can always see he’s trying to work on something, which is a great attitude.”
The result has been a highly successful evolution of Anderson’s skills.
“He is a very different bowler now,” said Cook. “When I first played against him, he bowled quickly and swung it into me.
“He bowls quickly now but swings it both ways, and it’s very hard to pick up.
“No matter how many times you face him in the nets, the reason he’s a world-class bowler is he can do that. His skill levels have gone through the roof.”
His wordpower is coming along too.
“I can’t tell you my first impressions because I played against Lancashire, and he called me everything under the sun,” said Cook.
“Then I went on an England A tour with him, and we never spoke.
“We were called up [in 2006] to play for England together from Antigua, to go to India, and we were sitting together on the plane. The only words he had said to me before then were swear words, and I was thinking ‘this is going to be an interesting 48 hours’.”
It turned out fine as apparently, in the much more recent past, has Broad’s recovery after having his nose broken by a Varun Aaron bouncer in the Manchester Test.
Cook expects Broad to be ready to take the new ball with Anderson although it is unclear whether he will be wearing some sort of facial protection when he does.
Broad bowled and batted in the nets on the eve of the match, and his captain said: “We think he’s going to be absolutely fine.
“He batted, he bowled his six or seven overs and didn’t get any pain from it.
“So we’re expecting him to be absolutely fine, and see what mask he pulls on (today).
“I don’t know what’s been going on ... but there have been quite a few masks.
“I’m not quite sure if he’s just going to wear it when he’s batting, or if he’s bowling, but I honestly don’t think it’s going to affect his performance at all, which is good.”