Someone has saved me by identifying my mystery plant as burdock and leaving me a helpful comment. To whoever it was, Thank you! I've heard of burdock, but have never really seen it growing. I was horrified by the description on this website. Such a weed. I've chopped it all down, bagged it up and it will be heading out to the trash, not the compost bin. Then I sprayed the stump that was left with a weed killer called "Perfectly Naturally Weed and Grass Killer".
I think I like this particular weed killer. The active ingredient is clove oil and the inert ingredient is vinegar. I used it over the weekend on some thistle, which now appears to be dead, dead, dead. So I finished up the bottle of it this evening on the burdock, more thistle, and the moneywort, which is making its first valiant comeback. I knew the moneywort would try to do so and so I haven't yet tried to plant anything where it was growing, as I know that I need to make sure it is all gone first. See this post for my opinion on moneywort.
Also, where the moneywort was there are now hundreds of little thistle seedlings also trying to make a go of it. I've sprayed them down as well. Hopefully this spray will do the trick, kill those weeds and we can all return to a blissful life in the garden, full of sweet smelling flowers, soft grass, and pristine weed-free beds. Ha!
I'm definitely going back to the store to get more of this weed killer!