I have a few of those trees in my yard.
Here in the Pacific Northwest, it's too cold for their seed pods to germinate naturally. They propagate best using root cuttings, and fairly easily with regular cuttings. You can literally stick a cut branch into the soil and have a fair chance of generating roots.
Cutting the trees at ground level (coppicing) the first season or two is common to get the roots established with young trees, and also when harvesting mature trees (and yes, they just grow back)
In some parts of the country they are considered invasive (Southestern USA IIRC) because they will propagate naturally with their seed pods. They also grow extremely quickly and can be difficult to remove the roots when you n longer want the plant.
I've had some of them for ~4/5 years(since they were copiced to the ground), and am somewhat familiar with them if you have any questions. I have a mix of older trees and new trees since the young plants make awesome garden plants with huge jungle looking leaves, and the older trees provide excellent summer shade in just a few seasons (they're blooming now, with light pink flowers)
The new leaves began appearing maybe a little less than a week ago, and are already filling out the trees. They really grow amazingly quick. A tree I copiced last year, with a full summer growth could reach as much as 18' to 20' here in Western Oregon. They slow down as they grow, I'm guessing my 4 year old trees are +30' now.