The valve seat has come out of the head and is now stuck out side its bore. #1 The correct repair is a new head ~ $110 or so list. or #2 You can try your luck removing the valve, peening around the area where the seat fits in, set the seat, lap the valve in , clean , reassemble w/ new gaskets or see option # 1...

And do a really good inspection and cleaning under the cooling fan shroud and sheet metal ducting on the engine.
The 31 series Briggs is somewhat infamous for loosening valve seats when the cooling air flow from the fan is blocked by debris or mouse nests.

In thinking about my response, there is also an outside chance that a throttle plate screw has come out and is lodged between the seat and valve. This has been a year for valve seats for me though. Mownies spot on about the importance of keeping the cooling system clean. 4 out of 5 seats come out I think due to heat build up.

Thanks for the responses. Looks like the original diagnosis was spot on. When I removed the head the valve seat was, indeed, stuck under the valve.

Now for the repair options...

Could you give me a little more detail on procedure #2? I'd like to get it running asap and ordering a new head would put me into next week. I already ordered a head gasket kit and it should be here tomorrow. Would this option require a new valve seat?

I am still curious as to the cause though. I checked for debris around the engine and saw nothing significant, except for the sporadic dirt dobber nest between the cooling fins here and there.

So... what's the best way to remove the retaining clip at the end of the valve spring without damaging it or myself?

What I do on aluminum is take a sharp awl and make 4 moderate punches at about the lower 1/3 mark where the seat will nestle in. (IE 12/3/6/9 o'clock) Then centered between these marks, do 4 more at about the upper 1/3rd mark. Support the head in this case so you can drive the seat in squarely until it bottoms. A sturdy socket would do that matches the outer part of the seat. Once the seat is in, you can stake the seat with a tiny punch for extra security around the outside of the seat. Repeat the above process after you wrestle the seat out again once you've realized you set it upside down... (k ;) Ideally you would then use some lapping compound and suction cup tool to help mate the valve and seat. Obviously, clean up is important.
If you don't have a c type valve tool at your disposal, you can do this by hand. You will have to rest the head on something solid on the head of the valve to hold it in. Push down the spring and cap assy and pull out the 2 tapered keepers. To reinstall, put a touch of grease on each half of the keeper then rest it in the cap part way at the top of the hole. Push the spring and cap down and then the keepers in place to seat. If you had an assistant at this point to slide the keepers in, it may go easier. Sure someone doesn't have a head on the shelf nearby? :) good luck.

I was able to get the valve disassembled and the dislodged valve seat reinstalled and lapped today. Not too confident on my staking job though. After examining the casting job on the head I was afraid to hit the punch very hard for fear of ruining the it. I guess time will tell if it holds up or not. Your instruction was invaluable and made the process seem fairly straight forward and simple. Thank you again.

My gasket set should be here tomorrow, so hopefully it'll be mowing again before dark (depending on Fed Ex's schedule).

P.S. Would someone happen to know the proper torque sequence and values for the head bolts on this engine?

One thousand words equivalent.
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Mownie, I really like your pics better illustrated! To wesak, glad the info helped. It doesn't take much to help stake in the seat. I use a tiny round punch on the outside, not a center punch type. It takes very little pressure, doesn't mar the surface horribly and create hot spots. you will also need to reset the valve lash as you put it together.

Well, my gaskets made it today. About 10 minutes afterward it began to rain. Go figure.

Since the mower is sitting in the same spot it was since the breakdown, beside my back porch, I decided to forgo reassembly until it stops. Maybe tomorrow's weather will be better.

Mownie: That's exactly what I needed, you have a way with words :) Thank you.

Tomplum: I used a pin punch also, instead of a center punch. Glad to hear that I might have a little common sense after all.

You guys are awesome, thanks for all the help. Maybe tomorrow I can put your wisdom to use.

The weather cooperated this morning so I was able to get everything put back together. She's running as good as she ever did.

Tomplum, mownie: I couldn't have done it without your help. If you're ever in my area, I owe you guys a beer at the least.

Now to figure out what's causing the new vibration when the blades are engaged...

:^) Cheers! (clink)

"Now to figure out what's causing the new vibration when the blades are engaged..." That'll cost ya 2 beers! Most deck vibrations come from the belt itself that I see. Something momentarily hold a blade and the drive pulley burns into the side of the belt. As tension is kept on the belt, there's your shake. Obviously, a worn/ loose this or that warrants an inspection so you know all is safe.