... is a Spanish Biretta with a tree in the middle of it. This is for a Spanish Philosophy Degree, apparently, thus explaining the need for a large brush on the top and a cascading fringe effect. And why not, we ask ourselves?
Put more respectfully and sensibly here:
Portrait of D. Juan Benlloch, seminarian graduate in Theology, Valencia, with Roman habit, white satin cape (muceta blanca), ring (anillo) and remarkable laureate bonete with silk fringe and handle / garland.
Ohhhh, so it's a handle...