In these side valve Briggs engines, the crankcase breather is vented to the carburettor.
The valve tappet cover has a one way valve and some baffles in it, and a hose that connects it to the carby. It would be worth pulling the tappet cover and giving it a cleanout, but as drew2229au says, the most common cause of this problem is combustion gas blowby past worn or stuck piston rings.
It is probably not worth paying a shop to repair it, if it needs rings.
Replacement with a new engine may be the best option, in that case. A new Briggs 550 series OHV 3.5hp will be in the $300 ballpark, plus fitting.
