David, your little insect is a thrip. I'm not surprised that they have found your little balcony plant.

Thanks Rhizo. The basil has been quarantined to its own corner of the balcony. I don't want to use any insecticides. I am trying to removal parts of the plant that seem to have the white residue. If that doesn't work, I may try to use an all-natural spray to treat them. If all else fails, my basil will end up in the trash which would be unfortunate as I raised it from a seedling.

I don't think it's necessary to discard it. Just buy some traps, or try something like neem oil, insecticidal soap or those eco-friendly vegetable oil solutions.

Are you sure that the "white residue" in that photo isn't just the stippling left behind after the insects have sucked up the chlorophyll? I'm pretty sure it's just part of the leaf...

The critter looks like a leafhopper to me. If so, when you disturb it, it will move sideways.