Is there anyway that you could remove an affected leaf and stem so that you can take a better close-up? I might be able to ID these little things with a more detailed picture.

Try this

Or this

anyone?

These things aren't growing on the leaves, too, are they? If not, I'm going to guess that they are adventitious root primordia. We see such 'aerial roots ' on lots of different kinds of plants....tomatoes being very familiar.

This is a guess, since I really haven't seen a picture that makes me certain. And if the leaves are also affected......all bets are off.

They are not growing on the leaves. So is it going to hurt the basil? What can i do to resolve it?

rhizo - I thought adventitious roots too. In fact I could have sworn I'd posted that but it seems not. Hollyhotpeppers - do they wipe off easily? If not I'd say roots. In which case there is no need to do anything about them. Or you could take some cuttings.

Yes they do wipe off pretty easily. Here in FL we have had a very wet summer with tons of rain an humidity.

If they wipe off VERY easily, rather than snap off, then they aren't roots. Have you tried breaking one open and looking at it under under a lens?

Unless Holly can provide improved images.....I give up, lol.

Do these things move or are they rather firmly attached to the stem?