Thanks to a botantically-inclined friend, the identity of my mystery plant is
Lamb's Quarters (Chenopodium album). A wonderfully cute name for a plant to show up in this fiber fanatic's container garden.
But it's not a plant, it's not a flower, it's not a bush, herb, fern or vine.
It is just... a really big weed.
So two nights ago I proceeded to unearth it from the giant blue pot. I had to hack at the soil with a trowel to get it to come out in clumps. It was a damn healthy weed with roots that had spread through that entire pot so out went all the soil, too. I had no chance of saving the coconut lining of the other container, either, so the whole thing was put in the trash.
The mystery still remains how these plants showed up in my garden. Was it a bad seed packet - labeled lavender but full of weeds? Or was it the potting soil mix (moisture control by Miracle Grow)? It wasn't birds or seeds on the wind since these plants were all started inside.
Oh well - it doesn't matter. The weeds are gone now. I'll be transferring basil to the big blue container and I hope to grow a formidable basil tree in it.