Burning oil at startup

[Beej '86 325es]

The last couple months I've noticed my car will occasionally put out a good size cloud of smoke from the exhaust at startup. It doesn't do this after it's been running for a minute or so, just for like 5 seconds after startup. It's definitely smoke from burning oil. Is this from leaky valve seals or something?

Not that I plan on dropping another dime on this engine anyway, but just curious.
Thanks.

[E30godz]

could be oil slowly leaking past the valve seals after the engine gets cold and they cool down?

[Beej '86 325es]

That's my best guess, it's only on cold startup, never when the engine is warm.