Most likely suspect here is a leaking head gasket. How this works is the head gasket leaks compression/combustion gases into the crankcase, causing excessive pressure which then tries to escape however it can.
The oil leak at the fuel pump breather means that oil has been forced past, or through, the pump diaphragm.
This is a somewhat common failure on the 28 & 31 series (yours is a 31P777).

Here is a link that might be useful: Post 'em pitchers

Thanks for the quick reply Mownie! Is the head gasket something fairly easy to replace for a do-it-yourselfer or should I seek professional help for this?

Mownie, I also checked the B&S diagram for the model you gave me. It doesn't specifically mention "Head Gasket" anywhere, but it does mention "Gasket - Cylinder Head" (part #796584). Is that what I should be getting?
Thanks again!

That is the part and the correct part number.
With a Briggs service manual, a person with some automotive or outdoor power experience will not find head gasket replacement too daunting a task.
It is required that a proper torque wrench be used to tighten the head bolts correctly and uniformly.
It will also be necessary to adjust the valves after replacing the head gasket, this requires the proper feeler gauges and you must follow a specific procedure when adjusting the valves.
You alone must decide whether you have the skills and tools to do the job.
E-mail me and I'll send you some literature, if you like.

Thanks again Mownie! Email sent..

I have read so many of these posts I am getting dizy.

Aug of 2011 I decided to have the head gasket change to stop the oil leakage from the NEW Fuel Punp Had it all set to go to the shop before going on vacation. Things got screwed up and the hired grass cutter did not cut the grass when i was gone.
So now I had to use my all cleaned up engine to mow the grass sevelal times.
I noticede that I was no longer loosing oil from the fuel pump. HELLO!! Since that time, 12 months ago, I maintain the oil level at the bottom line and have not lost any oil for the last 12 months. I think you are OVER filling when using the top mark. Cheap fix try it befor spending money.

Well, if you are using the top mark, but not fully seating the dipstick completely to the locking position when you do your dip test........you could in fact be overfilling the engine.
But if you are following Briggs' instructions and are fully seating the dipstick when you check the oil.........you are not overfilling the engine.

You can almost always tell when a NEW poster has signed up. 2 year old threads start getting answers/comments.