Your voicemail doesn’t have to be monotonous or impersonal. What you need is something that is unique to you but works in a professional manner. Professional voicemails are important, because they’re an extension of your personal brand, reflecting what level of professionalism you offer. Use these voicemail greetings for work or personal cell phone messages […]
Set up Visual Voicemail. If your carrier supports Visual Voicemail, you can set it up with these steps: Go to the Phone app, then tap the Voicemail tab. Tap Set Up Now. Create a voicemail password, then tap Done. Enter your password again to confirm it, then tap Done. Select Custom or Default. If you choose Custom, you can record a new greeting.

Oh - if anyone is still curious: I recorded the greeting via the phones custom greeting function, then called to listen to it from another phone, then turned off the phone and called again. Same message. I had wondered if just maybe the phone played the message when on, and the carrier played the message when the phone was unreachable.
21. "Hello, you've reached [your name, the office of X company]. The team is currently out of the office, but we'll be back on [date] stuffed with good food and eager to speak with you. Leave your name, number, and — if you're so inclined — your favorite [holiday dish, Thanksgiving tradition, etc.]"