Extra mustard refers to a certain unnecessary and generally amusing additional emphasis that Lars or Joe (or, occasionally, a guest) will put on specific words or phrases. There is no particular reason for this other than subtle humor.
Often Joe will over-pronounce a word beginning with "wh" as if it was spelled beginning with "hw". While common until even relatively recently, said pronunciation would in 2019 be considered old-fashioned if not outright archaic. It can be heard mostly from adults three generations before the current one.
Likewise, Lars will generally pronounce the letter H as "haitch". This is a habit he picked up from watching several British content creators, and is virtually unheard of out of extremely specific regions of England.
On episodes with Richard Quiner, the hosts or Richard himself will humorously note that a way of pronouncing his full YouTube title "Game Master Richard Quiner" can make it sound more like "Gay Master Richard Quiner". This was the source of significant amusement when Lars first pointed this out to Richard on an earlier episode.