Well, @
jplake, WELCOME to ....The Forum ...... and BRZ ownership ...... and to all the little sounds these cars make..........
Since your car is new and still under warranty, I would suggest you take it back to the dealer and ask them to check it out.
Meanwhile, you may wish to check and make sure all the lug nuts are tight.
It could be lots of things from an under panel lose, to a brake caliper being lose, to lose rear axle nut, to a front strut needing to be tightened up, to a....a....a.....a........
Then again, maybe the suspension is just stiff from being new.
I hope you get it sorted out soon.
humfrz