Like justincredible said, the buildup is on the valves themselves.
From what little I understand about engineering, this issue is rampant in Audi FSI engines (as well as BMW/Merc, from what I’ve been told). Because FSI is an injection system that injects fuel directly into the cylinder itself, fuel never comes in contact with the “top” of the valve, which is apparently necessary to clean the valves. There are other cars with FSI that don’t suffer this issue, so I’m not actually sure why exactly this happens.
I’ve heard of carbon building up in as little as 5,000 miles that will actually impact performance. It seems the issue was resolved in the later models, and isn’t as bad in cars with forced induction, but definitely still happens. The RS4 guys have it the worst from what I can gather, and I’ve even read some stuff about a class action lawsuit as the buildup isn’t denoted in the scheduled maintenance published by Audi, but inarguably affects performance. Some dealers won’t even acknowledge the issue until your engine throws a code related to it, but there are hundreds of cases that I’ve personally seen people benefiting from doing the clean preemptively.
If you tackle this yourself, I’m far, far from an expert, but do NOT let any carbon fall into the cylinders.
As to how the carbon is actually removed, when I had Audi do mine, they used a solution of some kind to soak the valves and actually had to manually remove a lot of it as well. Might be worth a call/visit to see if they can sell you some or tell you what it is. I doubt it’s very specialized, tons of liquid compounds bond with carbon that shouldn’t present an issue.
Hopefully this helped. This is mostly info I’ve gathered from reading posts on this forum.