My Sony smartphone has an unusual TRRRS (Tip-Ring-Ring-Ring-Seal) connector, allowing it to use very reasonably priced noise cancelling headphones (Sony MDR-NC31EM) that have an extra microphone in each earphone.
I found that the Sony app Sound Recorder allows selecting recording directly from these two microphones, and are great for binaural recording, and I gave it a go walking along a few busy streets. You can listen on YouTube and Soundcloud: