I had that problem last year, and have it again this season with my 9hp Briggs. My Snapper dealer tells me that the additives in modern fuel are damaging the carb needle, thus preventing the fuel from cutting off and allowing it into the crankcase. I replaced the needle and seat last year and had one mowing season without the problem. He tells me that this is an ongoing problem and he has seen the needle go bad again in as little as two weeks and there is no current solution other than needle/seat replacement.
If you replace the needle and seat yourself, make sure you completely drain the crankcase of fuel/oil. Fill with new oil, drain, and repeat. I turned my crank a few times with the first oil change, not starting the engine, but to rotate the parts into the new oil, then drained it all, and refilled. Fuel breaks down the oil and you want to make sure you get as much fuel out of the crank possible.
Replacing the needle and seat (with a needle and seat kit) is a pain, but much cheaper than paying someone.
Clayton Adams, March 2008