cold start okay then restart it, it runs very rough for a minute or two then drives fine?

I have a 1988 e30 325i in Australia. Drives great upon first start up even when cold but if I warm it up, stop for 10-20 minutes engine off then restart it, it runs very rough for a minute or two then drives fine. The first couple minutes it is undriveable and likely to stall if I try to take off. It very recently had a full service and timing belt + plugs. What could be causing this issue? P.S. I love your workshop guides and the parts even with shipping are about half the price what BMW in Australia is charging.

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[Nick at Pelican Parts]

Sounds to me like you might have leaking injectors flooding out the engine on a hot restart

- Nick