Have you checked for caterpillars? I've had some show up this year and they do like basil. About the others, I don't know. Thankfully never had rats.

Didn't see any evidence and the critter ate everything but the stem. We have packrats here in Arizona, and you are lucky not to have them. Our native plants give them lots of food with pinyon, juniper berries, acorns, etc,

Check the stem where it is bitten off. If it is a precise diagonal cut, it is likely a rodent.

Well that's no bueno. Hoping I don't get them!