OK. It just so happened that my 335i was cranking slowly, so I took it in yesterday and they ended up replacing the fuel pump. Here's what the invoice/work order specified:
C/S: Client states vehicle is hard to start in the mornings.
Failure of high pressure fuel pump. Performed vehicle test and found code 2FBF. Refer to SIB 12-55-06 checked I-Level E89X-08-09-520. Target is E89X-10-03-504 needs programming. Checked low side fuel pressure 5.8 bar higher than required 4.75 bar. Performed programming with CAS and readapt DME and initialize szl. No change in condition. Submit TC PUMA case # XXXXXXX and PUMA approved HPFP and admin payment. Removed and replaced HPFP and cleared faults. Verify repairs.
13-51-7-613-933 RMFD High-Pressure
13-51-7-613-933 Core Return
11-61-7-547-242 Set of Profile Gask
I'm sure there are some on this forum that can make more of this than I can, but in the end I got another
fuel pump and a reprogrammed computer. FWIW, I have not noticed and difference in car performance (positive or negative).