When I accelerate around 2500+ rpm my car will hesitate a shoot out a thick cloud of white smoke. I have a 2009 328i. It smells like burnt oil as well and Im losing oil. I don’t understand
I have had this on my daughter's 2009 328I. Its is either the PCV diaphragm on top of the valve cover or one of the two checks inside the valve cover has failed. Oily vapors from inside the valve cover is being sucked into the intake manifold. You can check the PCV diaphragm by putting a 1/8" tubing on the PCV cover nipple and suck a vacuum on it. If it does not hold a vacuum then it is bad. If it does then it is a bad check valve inside the cover.
Her 328I had both of these things happen. First successfully replaced the PCV diaphragm which was bad. But that did not solve the problem, so I replaced the whole valve cover. That solved the problem totally. One of the check valves inside the cover was broken by a PO probably changing the valve cover gasket, it had been siliconed back on and fell off when I removed the cover!! Just go ahead and replace the whole valve cover to be sure.
That's most likely your CCV (Crankcase ventilation) Very common problem with inline 6 cylinder BMW's. I believe thats the N52 motor in your car.