Honestly, the easiest way I’ve found is with the Nexus Root Toolkit and doing Flash Stock + Unroot with the “No Wipe Mode” and “Force Flash” boxes checked.
I find it easiest to just download my current build factory image and flash that.
This returns the phone to stock, but without wiping it, allowing it to download and install the OTA updates.
I’ve never been able to properly sideload OTA updates, so I find this way more convenient.
(Didn’t work for the Marshmallow update for some reason. Ended up sideloading it manually using adb.)