2001 bmw 540i have code 1343 not sure what to do next

P1343. Misfire Cylinder 1 with Fuel Cut-off.
I would start looking at the air intake for leaks first. Make sure the intake boot isn't torn anywhere, inspect it throroughly around all grooves for cracks.

Also check the crankcase for excessive vacuum by removing the oil cap with it running, listen for idle speed change, and excessive vacuum entering with the cap off.

This would indicate the crankcase vent valve has failed under the intake.

It can be replaced without removing the intake, it's kind of a pain. You will need the valve and the attaching hoses since they will need to be broken to remove the valve, and they get brittle with age.

The valve is located under the intake, slightly forward of the throttle body. I wouldn't try do do it unless you're really mechanically inclined, its kind of tough.
The part # for the valve is 11617501566.

Then the hose part #s are:
11611432559
11157532649
11617504535
11617504536




I hope helps.

Who told you the code? you should be able to go to Auto Zone and they can tell you what it is for free, and may have the part to fix your problem.