Even if the contractor was only responsible for the framing, if he
framed it so it can't be ventilated, then he framed it incorrectly and
it should be fixed. Whether the engineer shares any liability is not
clear--did he provide construction drawings, or did he just size the
beam etc?

When I've encountered this situation, I drop the beam by and inch or
so to allow air to pass over it. (that is the points of the rafters
are above the beam). Probably too late for that....

You (or he) might be able to sawzall a bevel on the LVL to allow air
to pass over the beam (talk to the engineer first, though). Either
that or drill some holes through the upper corner of the beam. The
other option is to look into a hot roof. That is going to depend on
your local building department.

Many people, myself included, feel that roof ventilation is not always
needed, IF the vapor barrier is properly installed. Mind you, I'm
talking about a cold climate here. However, if your building
department doesn't agree, it doesn't matter what my opinion.