Sounds like there is too much air in the flame. Is there an adjustment for it?

Ours does this too (outside grill). Mr. Clean eraser helps with the clean up.

I thin bikey may have it backwards. Soot generally means incomplete combustion, which means insufficient air. There may be an adjustable shutter on the line between the adjusting valve and the burner (close to the valve) that has gotten knocked out of its proper place and restricted air flow, or some leaves or other foreign object could be causing a similar problem.

Squirt some dish soap on a paper towel and wipe the outside of the pot before you cook on propane. It won't stop the soot, but it wipes off easily when you're done.

sbpoll is right about the dish soap. My husband has always done this when cooking outside. I think it's an old Boy Scout trick.

Jon is right....

Or...the range was installed with a connection for natural gas...and not propane....this happened to a neighbor...and the soot was indeed the result and how they discovered the problem.

Whatever, have this checked ASAP...propane is NOT supposed to leave soot on anyhting..and that is a major indication that something is not operating properly.