You're clearly curious about it and genuinely interested, so you could ask him if it's ok to ask him about his stutter. If he doesn't want to talk about it then don't push it, but if he's got a non-judgemental ear he might be happy to open up about it. And yes, a chat over a beer or coffee where there's no pressure to get back to work could be a good time to do it. In work there might be no real escape.