Answer: I'm guessing that the tree in question is Paulownia imperialis, the Empress Tree. It's native to China and the growth habit is as you describe. The leaves are light green, heart shaped, and 5"-12" long. Brown flower buds the size of small olives for in autumn and persist over winter, opening before the leaves emerge in the spring. The flowers appear in 6"-12" long upright clusters, are lilac blue, and extremely fragrant.
You can start new trees from the seeds in the pods by planting each seed just on the surface of moistened seed starting mix and covering the trays or pots with plastic wrap to help retain moisture. Place in a bright spot (out of direct sunlight). Seeds will germinate in 30 to 60 days when kept at 55F-70F degrees. The seedlings will grow fast, but the new little trees won't flower until they're about 7 years old.
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