Some cold start miss/pop isn't that unusual in BK, I can only think of once I got a solid backfire from mine (BK) and that was in stop start traffic. I'd suggest getting an OBD log onto it, possibly could be bad fuel - have had that once with my BL. I'd be eyeing knock retard values, fuel pressure, manifold pressure, long and short term fuel trims and AFR. That's where I'd start. Some other members might have some good suggestions for what should be logged in this case.
If bad fuel i.e. had toluene in it or something can take a few tanks to be completely rid of it - that's what I found anyway.
Spark plugs pop to mind as something that might need checking. A _careful_ clean of the MAF wouldn't go astray...
"Blue Meanie" 2007 Aurora Blue MPS 3 - 18x8.5+44 SSR GTX01 - 235/40R18 Michelin PS5 - 3.5" ETS TMIC - CPE stg 2 mount - HKS/CPE BPV - 2XS inlet - 2XS short shift - Corksport turbo manifold - HT 98 octane tune - Leather/Aluminium handbrake - Momo shifty knob - 7" touchscreen - JDM Mazda Retractable dashtop screen assembly - Bespoke Raspberry Pi Android based GPS/Carplay and instrumentation - 36AH reserve battery and C-TEK isolator - TEIN Street Advanced coilovers 1" drop - Superpro bushings - 220Kw/410Nm.
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