While watching Quahog 5 News at The Drunken Clam, Peter, Joe, and Quagmire hear that notorious heroin mogul Bobby “The Shirt” Briggs – (an apparent reference to the Twin Peaks character of the same name) who began a minor drug-running operation in 1996 – has finally been caught after fifteen years on the run.
However, Kevin informs him that Tom Tucker is reporting a breaking news story about Bobby Briggs escaping police custody during a prison open house.
When Joe's direct questioning fails, Quagmire cites his ability to communicate with strippers, extracting Bobby Briggs' exact address through a sexual osmosis he calls the "Vulcan V meld".
A rooftop chase ensues, which results in Joe's being able to survive being dropped several stories by landing directly on his legs.
Nonetheless, Bobby Briggs is able to escape by hiding behind the bus on a suddenly appearing Extreme Makeover: Home Edition.
Realizing they have been arrested by corrupt officers (and probably the ones who pretended to arrest Briggs and then helped him escape from police custody during a prison open house in the first place), the guys enlist the help of Quagmire, who manages to free them from handcuffs using a combination of his Swiss Army Penis and acetylene torch penis, and the three steal the police cruiser.
Having reached the border, Joe, Peter, and Quagmire wait in the scorching heat, before realizing it may be days until Briggs comes through, as he is presumably traveling by car.
After passing some time at El Paso's Pershing House, the trio check traffic until Briggs arrives.
From Quagmire’s comment through clenched teeth to Peter to not volunteer him for things like this... to getting to El Paso a couple days ahead of Bobby Briggs... to the aforementioned continuity nods, this was written with a relative intelligence for the series.