I am thinking its a single cylinder Briggs on a Timecutter-judging by the muffler mount strap.
What you see is, I think, burnt motor oil deposits. I guess with 600+ hrs on it the guide is not tight as it once was and part of the exhaust gas is following the exhaust valve guide back into the rocker chamber. (no valve stem seal on exhaust, if I remember correctly.)
I wouldn't worry about it too much. At those hours You have pretty much the expected service life out of the engine and its not practical to replace the head or put a valve guide in it just because of those black deposits. I can tell you manitained it well, you never would have that many hours on it if you hadn't.
Just keep the cooling fins clear of debris and keep the oil level above the add mark and don't worry about it until someother problem crops up.
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