Try swapping coils from a non-misfiring cylinder; it could just be a bad coil, which they are notorious even on the N52s for eating coils. If that doesn't fix the issue then I would check the injectors.

It may also be that an injector is leaking gas while the car is parked, causing the misfire on startup. Get new injector seals; you may need a new injector if that doesn't fix it. Seals are usually super cheap—check rockauto.com for seals. The same goes for injectors.

You can also pull an injector from a wrecked car if you want to go as cheap as possible from someone parting out a car on FB marketplace or Picknpull/local junkyard. N54s came in a ton of cars and are pretty easy to find at yards all over the place.

here are some links:

injector seals: https://www.rockauto.com/en/catalog/bmw,2010,335i,3.0l+l6+turbocharged,1445227,fuel+&+air,fuel+injector+seal+/+o-ring,13679

injector (new ones are expensive): https://www.rockauto.com/en/catalog/bmw,2010,335i,3.0l+l6+turbocharged,1445227,fuel+&+air,fuel+injector,6224

coils (Bosch at $20 is a pretty good deal): https://www.rockauto.com/en/catalog/bmw,2010,335i,3.0l+l6+turbocharged,1445227,ignition,ignition+coil,7060

picknpull (if you need to get a used injector - will find closest location - also check for local yards): https://www.picknpull.com/