Howie Roseman
Most of Roseman's success has come with Jalen Hurts, and I consider Hurts a very good to excellent quarterback. They had some bad seasons early on in the true Roseman era.
That said, what makes Roseman an exceptional GM is that he makes the hard decisions that 99% of GMs won't make, i.e., moving on from Wentz, moving on from Pederson a few years after winning their first Super Bowl. Though, it's unclear to me how much of Pederson leaving was Roseman's decision or Pederson wanting out.
Ozzie Newsome before Flacco is the only one that comes to mind. 2001 Ravens had the best defense since the 85 Bears.
Alright, we've got 1 GM not tied to a QB so far.