When we pick up the phone it beeps as if we have messages but when we call in we don't have any messages.
Try, leaving yourself another voicemail message from another phone, then going back into the voicemail system and deleting it, using *? to exit,
Hang up after it disconnects the call, give it a minute, and pick up your phone again, see if the stutter is gone.
Did Kevin's trick work? It's possible that your phone just needed to connect to voicemail to let it know that there weren't any messages.
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