This plant grows in some ornamental gardens here in Ontario, Canada, USDA hardiness zone 4. It is somewhere around 8 feet tall I would guess, and the leaves are huge. Looks too exotic to be hardy here but I'm presuming it must survive the winter or else they dig it up and winter it indoors (which would be quite a task). I've seen it in the same spot several years in a row, though. I've never seen flowers on it, so if it flowers in this climate it is at a different time of year. Thanks for any ideas.

Paulownia tomentosa, an invasive tree species that spreads by seed.

Thanks, Lori, you're good! Yes, you're right, I can see it now. I'd never have recognized it without the flowers. Zone 4 would seem to be out of its listed range, perhaps city heat island effect (it's in Ottawa) is mitigating. I assume it is killed to the ground in winter and likely doesn't flower (hence the extra large size of the leaves) and therefore can't spread by seed here. Can't find it again now but I did find a reference to its being killed to the ground in eastern Canada.

I have a friend who coppices these every year. This keeps the leaves huge. She uses them behind her flowers. It looks great. This also keeps them from being invasive.

I have been seeing these large leave plants growing at the roadside of Charlotte, NC. They have no flower, so far.
I took a photo of these plant today, but it would not load here. In my country, Viet name, there was a flower plant, which also has similar look of the leaves, named Quy.
Quy flowers are only in white, with lots of flowers on a stem like hydrangea would be, but Quy flowers are heavier because they are like extra large, double jasmine, also very fragrant.
For similar large leaf flowered plants, google tropical hydrangea.