A species of Petasites or Tussilago, more details needed to tell them apart.

I think it's Tussilago farfara (AKA Coltsfoot)! I do recall seeing a couple of those yellow flowers, but there certainly weren't very many, and no where near how many leaves and individual looking plants there are now.

I would love to provide more information/take some photos today and post them. What information would you need to make a definitive diagnosis?

Does anyone know how to get RID of this horrific thing? I just read that it's listed as a noxious weed and banned in several US states.

I suppose you have tried pulling them out?

Since you live in Montreal, you can only get non-selective herbicides are such as Round-Up or Wipe-Out. Be careful not to get any of the spray on the surrounding vegetation. It will take several days to see results, but I think that should kill off most of it and you can reapply if any come up again.

If you prefer not to use a herbicide, then use a vinegar and salt solution. Try to get some Heinz Pickling Vinegar which has a higher concentration of acetic acid than plain white vinegar.

You could also burn the weeds with a blow torch.

Whichever one of the above methods you use, I would first trim about half of the leaves and then treat the remaining leaves.