Sounds like Paulownia tomentosa (Princess Tree).

Larry

I had one in my yard on the Eastern shore and was never able to identify it. I cut it down to the ground and the following year it grew back two storeys high. very soft wood, HUGE leaves, no visible flowers.

I grew up in Baltimore County and enjoyed it in our wooded yard. Commonly also called a Royal Paulownia. It will grow house-height in one season prompting my kids to call it the jack-and-the-beanstalk tree!