You didn’t ask, but an EID is a serial number that’s unique to a device that is eSIM enabled. To find it open your Calls app and dial *#06#.

This opens an overlay with information specific to your device. For iOS, Tap "Settings" > "General" > "About" and scroll down to find your EID. For Android, Tap "Settings" > "About Phone" > "SIM Status" > "EID". For your smartwatch (how fancy of you) you should be able to find this in the settings or from the app on your companion mobile device.