Smoke colors can be deceiving. Black too much fuel, Blue burning oil, White caused by moisture. I would check the fuel first to make sure you don't have water in the tank. Second I would start the engine and let it run for 30 minutes, making sure that it gets and stays at operating temp. This will burn off any moisture which may be in the engine due to winter storage. If you can run the tank dry and then check with fresh fuel, it would be even better.
Ha ha, couldn't help "commenting on a comment" in this string: I love your disclaimer, Rivets, about book learning! I used to score 99's in several areas of the old "Iowa Basic" tests we used to get, and even in top 1/2 percent in "Pre-SAT" test but I got so disgusted with the tests, because I saw there was NO CONNECTION between my scores and any success in the world, though maybe I'm a good "mocking bird" knowing how to knock off all the other birds' songs, I cant stay away from the CATS, its always the pretty mocking birds we see torn up down here, unlike the grackles and bluejays and every other buff bird which doesn't get caught, so that doesn't sound too "smart" to me... Plus I'm dumb as a squirrel who can't recall where he buried his nuts! (acorns, 'scuse me).
Anyway, I feel this "smoke from carb AND exhaust likely IS a head gasket, and asked at a local "outdoor power" store, where they said breather would account for carb oil/smoke, NOT exhaust...(sounds like flu with diarrohea and vomiting to me!) My Honda air cooled (21" push mower) engine may have the same head-gasket induced problem; and white smoke sure persists after oil is spewed into a hot muffler. Sort of like an insect fogger! (if only it would kill insects, not make your customer think you were Jed Clampit) (sp?) Regards, Mr. Rivets! - I'm only seeking out the Briggs engines from my FATHER'S generation for my biz now; seriously, I'm not rich and I'm hard on equipment. Leave the OHC engines to the Mustang and sportscar crowd. (this white smoke not from water o'course, its air cooled). But of course the Environmentalist Crowd may have driven these manufacturers to make OHC engines, for all I know. Maybe the reliable ones from "the day" are not as clean, or something. Though broken gaskets and smoke don't sound "clean."!