As England's longest-serving Test captain, Cook has had plenty of big days at the home of cricket and he elevated this inaugural county decider with a superb 131 not out.
Somerset had been delighted with their 301 all out, reckoning it to be at least 50 above par on their initial estimates, but Essex were well on course to trump it on 196 for one at tea. Tom Westley was in the supporting role on 51no in an unbroken stand of 169 for the second wicket.
Cook, who scored 1,937 Test runs at Lord's including four centuries, looked every inch the international star he was for a dozen years before his retirement in 2018 dominating an attack who laid waste to their rivals in the group stage of this competition.
The average first-innings total against them in the five previous matches was just 119 and the average time needed to bowl the opposition out was just over 46 overs. Cook single-handedly went past both figures, batting with a freedom and elegance that did not always follow him on the biggest stage.
The qualities that made him the most prolific run-scorer ever to don England whites were predominantly discipline and diligence and, while he certainly needed those to come through a challenging new-ball blast from Craig Overton, he was soon stitching together an unusually pretty innings.
His trademark flicks off the hips and touches into the on-side were all present and correct whenever the bowlers' strayed in line but he peppered the cover boundary with ease too – repeatedly stroking the ball to the ropes with increasingly precise placement.
Overton and Josh Davey had started well, putting both Cook and Nick Browne on alert in the first 10 overs. Browne edged Overton's first ball of the day just short of slip, with Cook hitting fresh air with a couple of wafts outside off stump.
On two separate occasions Overton bellowed in frustration as Cook hung on, once just clearing gully and then nicking in front of the cordon. It took a change of bowling and a change of angle – Lewis Gregory going round the wicket and getting Browne caught at slip for a scratchy eight.
Cook soon bedded down, though, serving notice of what was to come by punching Gregory for a pair of sweet hits through cover, with him and Westley seeing the score to 79 at lunch.
They made hay in the afternoon session, adding another 117 without being parted. Westley was fortunate to survive a huge back-pad lbw shout from Gregory on 30 but Cook was in his element. He contributed the lions share of their partnership – contributing 64 in the 100 stand and 99 in the 150.
Somerset's attack was beginning to look a touch one-paced and it took 47 overs for Tom Abell to introduce spinner Jack Leach, who did not play at all despite 10 weeks in the England Test bubble this summer.
He served Cook a loopy full toss on 97, with the 35-year-old gratefully clubbing it through point before raising his bat to the pavilion.
Westley followed to 50 just before tea, with Somerset in need of a change in the evening.