First, roast your veggies: Spray two rimmed baking sheets with cooking spray.
Toss sliced veggies with olive oil and spices, then spread them out in single layers on the prepared baking sheets and sprinkle with shredded Parmesan.
Bake at 400 degrees for 25 minutes, changing oven racks halfway through, then remove roasted veggies from oven.
Now, assemble your paninis: Combine olive oil and Italian seasoning. Make sure rolls are open, then lightly brush the outside of each roll (top and bottom) with the seasoned olive oil.
Stir balsamic vinegar into whatever is left of your seasoned olive oil, then drizzle a little on the inside bottom of each ciabatta roll. Add one slice of provolone to each, top each generously with roasted veggies, and then add another slice of provolone and the top of the ciabatta roll.
Lastly, grill your paninis: Place assembled sandwiches in a grill pan or large skillet, press, and weigh them down with a press or large cast iron skillet.
Leave weight on top while you cook your paninis over medium heat for 3-4 minutes each side, until nicely browned and cheese is melted. (Do this in batches, depending on the size of your pan.)
Notes
If you have a panini press, use that instead! I used my smaller (less heavy) cast iron skillet as a weight since it matched the size of my grill pan, so just added a couple of cans of veggies inside it for extra press. If some veggies fall out while you're pressing the paninis, put them on back in your sandwiches when done or enjoy them on the side.