How about posting the model number of the engine since most likely they didn't build the engine unless it is a larger mower with the gas kubota. Also the model of mower can also help us determine what could be the issue.
Generally this will be from oil pooling in the combustion chamber when the engine is not in use.
Things that cvause this
1) worn or cracked ring
2) oil level too high
3) crack in the head
4) worn valve guide .
5) blocked drain in the head
7) leaking head gasket
if it's been hot, good possibility that the cylinders are egg-shaped, tapered, worn, and the pistons are trashed as well as the oil rings--all will cause smoke on cold start. Sometimes they'll clear up when hot because the exhaust system gets hot enough to cause the oil smoke to subside, and sometimes as the pistons/rings heat up and the gaps close due to thermal expansion, it'll also reduce oil smoke.
I have seen all of it.
Change oil first, if it clears up fine. If not, prepare to rebuild or replace the engine.
