The guys hit up The Pendry West Hollywood for the Talent Resources Sports bash in Los Angeles following the awards show ... and for some reason, Edey decided to test his reach against the UFC's best heavyweight.
The two traded a few jabs while cameras snapped away -- but don't worry, it was all completely in jest ... Edey's definitely too smart for that!!!
Following their impromptu shadowboxing session ... the fighter and the hooper posed for pics together -- and then partied the night away at an event that was packed full of celebs.
They all had a lot to celebrate too ... as the ESPYs were a huge hit.
Pat McAfee crushed it as the event's de facto host ... Chicago White Sox pitcher Liam Hendriks won the Jimmy V Award for Perseverance and delivered on awesome speech afterward -- and Hamlin had the moment of the night when he emotionally gave the Pat Tillman Award for Service to the Bills training staffers who helped him keep him alive following his in-game cardiac episode.