Defender Shaun Brian’s first-minute opener lit the blue touch paper as Hammers ruthlessly put to the sword the Premier Division’s backmarkers on Tuesday.
Osborne scored twice either side of efforts from Dominic Allen and Cook before the interval. Cook grabbed two more after the restart, while Osborne rounded off the scoring from the penalty spot late on.
The deadly duo netted no fewer than 51 league goals between them for Kemp’s Christchurch last season before following their manager to Winchester City over the summer.
Another 12 strikes followed during their brief stint at the Denplan with Kemp confident the reunited net-busters can continue their fine fettle at the County Ground.
Discussing the double act, Kemp told the Daily Echo: “I think that takes them to something like 31 goals between them in all competitions this season. It is an incredible record but nothing surprises me with those two.
“They have achieved massive totals over a sustained period in the Wessex League and I could not name a more complete pair of strikers at this level.”
On the match, Kemp added: “It was a fair result over the 90 minutes.
“We scored within a matter of seconds but Romsey did okay for the next 15 minutes.
“They were mobile going forward but quite poor at the back and the difference was we stood firm when they came at us and put them to the sword when our chances came.
“Being 5-0 up at half-time, we didn’t want anything silly to happen and, fortunately, we went straight out and got the sixth.
“It was a bit of a procession after that.”
Hammers: Rockingham, Penny, Hester, Brian, Walker, Corby, Rowe (Sturgess, 61), Allen, Martin (Cole, 65), Osborne, Cook. Unused subs: Biles, Diaper, Haysom.