We are all familiar with the common eaters, but this is new to me. This is a beetle, yes hard shelled, perhaps 1/4" at best, very round. dk brown. I noticed 'dirty' areas around some new growth of basil. As it didn't just wash off, checked again. A Beetle! As I am being more watchful, checking 2-3/day. They are in just one area, so far, but I am perplexed. I can find the beastie and destroy it, but know it has babies not far behind.
Sorry, don't have pics, but anyone with beetles on basil may have a clue!