I was hoping for more guesses, but I guess I'm out of luck. So I'll just have to tell you what I'm making. Yes, they could hold umbrellas... folded up ones, anyway. And if you were feeling really silly, I guess you could wear one for a hat. ;-)
But really, they're storage buckets. Nice sturdy ones. In fact, I laid a couple of books on the top of an uncuffed one, and it didn't collapse! They're 8 inches in diameter and 11 inches high uncuffed. So they should hold a lot of 'stuff' (umbrellas? toys? knitting? you-name-its?).
They can be used either way, but I think the cuffs make them even cuter. And the cuffs could be folded to any size you want, to make the bucket any height.
It's been kind of a hair-pulling experience, trying to figure out how to work with that heavy interfacing, but I guess I've got it worked out now. I mailed the first shipment to Jess, so if the post office cooperates, she should receive them today, and they should appear in the Etsy shop tomorrow.
And I'm busy making more, with many fabric combinations! Fun!
Late addition: Here's another one, in a different fabric.