UFC star Travis Browne is telling TMZ Sports exactly how he hunted down the people suspected of burglarizing the home he shares with Ronda Rousey ... and why he held back from beating their asses. 

As we previously reported, cops arrested 2 people for breaking into the UFC star's L.A. area home in April and raiding the place -- taking everything from jewelry to guns. 

Browne says he and Ronda took matters into their own hands at first -- with Travis personally locating the perps at a nearby skate park. 

"I was staring at them like, 'You motherf**kers!' You're lucky that I have the [self-control] to not beat the dog sh*t out your ass!" 

Browne says he smartly went to cops -- and one of the officers asked him what he'd like the punishment to be for the suspected ring leader. 

"I was like, 'How about give me 5 minutes with him alone?'"

Obviously, that didn't happen -- but the good news for Browne, he can unleash the fury all over Alexey Oleynik at UFC 213 in Las Vegas this weekend.