Although the photos are not explicit, what I see in ordinary carpenter speak is a header carrying crippled ceiling joists that overshoot the plate forming a cantilvered or perhaps a jettied support for the rafters. The technique of joining rafters to ceiling joists is not rare, using headers and cripples in a roof system is common but an entire roof system of headers and cripples is unique to my point of view. Since I do not see sprockets, brackets, stitching or dragons why not call it for now a Rooster Beam.