The experiment with the brioche dough to make buns worked!  I patted out the dough on a floured counter and cut them out with a big biscuit cutter.  I let them rise for about 45 minutes and then baked at 350° for about 25 minutes.

They made excellent panini!

Mayo and dijon mustard, sliced ham, roasted red peppers, and fresh mozzarella.

Simplicity.