Well, when I was out watering today, I finally identified the culprit:
Can you see him? How about now?
I have no idea what type of insect this is, but he blends in so perfectly with the leaves of my poor basil plant, he's probably been there all along! As far as bugs go, it's really quite beautiful; leaf shaped and with an iridescent sheen that catches the sunlight. He's so cool-looking, that I couldn't bring myself to flick him off of the plant, so I guess I'll have to settle for sharing my bounty. Surely there's enough basil for us both... right?
(By the way, if any of you do know what type of bug this is, I'd love to find out!)