I second the suggestion of Melia azedarach. I like the flowers and their scent, and the shade is not too heavy (it allows other plants to grow beneath). It self-sows, and can be grown by hand from the (rowan-like) fruit quite easily. I concur that it grows quickly, and spreads to a reasonable width early, too.
With a Morus (yes, choose a non-flowering/fruiting clone), you could train it over a metal or wooden structure to make as perfect as umbrella as you want, pruning so that it gradually comes to form its own wooden frame. After a few years of such pruning, the original framework could be removed to make it more attractive (save for some parts that might be needed to keep it secure against its weight and the wind).
Another suggestion: Delonix regia (click
here for pictures and some more discussion); less hardy than those above but with more spectacular flowers. It leafs out a little late, in my experience - which can be good if you want to grow spring flowers below it, but not so good if you need spring shade.