After starting his senior career with lower-tier clubs Virum-Sorgenfri and Gladsaxe Hero, Aabech moved to Lyngby Boldklub in 2004 where he grew out to become a key player.

During his tenure at the club, his reputation as a goalscorer grew and, together with Tobias Mikkelsen, Mikkel Beckmann and Christian Holst, he formed a formidable offensive, which played a major role in Lyngby's promotion from the 1st Division to the Superliga in the 2006–07 season.

[4] On 13 August 2014, Aabech left Nordsjælland again, as he had been dissatisfied with the lack of playing time under the new coach Ólafur Kristjánsson.

[5] As a result, his contract was terminated, and he commented on the following on the episode: "It's actually quite simple for me, I want to play more consistently, and I had no prospect of that at FCN, as there are many good players.

"[5] Aabech signed a one-year contract with AGF as a free agent on 18 August 2014 and joined the club at the same time as new teammate Darnel Situ.