That's a Paulownia tomentosa, aka Princess or Empress tree. Native to China but naturalized through NC and considered to be invasive and weedy. I've heard the wood is valued for furniture, musical instruments, etc, and they can look pretty amazing when coppiced to promote growth of those huge leaves, but I take them out if they grow in my garden because they outcompete just about everything.

They were the original wood used for disposable chopsticks. 20 years ago or so there was a shortage in Asia and people were actully sneaking into Botanical gardens and parks along the east coast to steal them and ship them back for big bucks. Plastics came to the "rescue" chopstick wise and now no one notices the invasion. As bad as Kudzu.