I found it hard to summarise this in the title, and I thought a few examples would illustrate what I mean best:
"Well known local celebrities include Alan Bennett and Barry Cryer" (lead up)
"Wait a minute: Well known local celebrities include Alan Bennett, and Barry Cryer used to know his milkman". (Extra information).
"'Open fire!', roared the Colonel." (lead up)
<Gunshot sound effects> (reaction)
"Yes I do love an open fire, he went on, warming his hands by the blaze" (Extra information, in this case laughing at the expense of whoever's in charge of sound effects).
I hope I've made myself clear as to the type of comedy I mean, I'm just wondering whether it has it's own name.