Preheat oven to 350.
Peel the eggplant, then use the coarse side of a box rater to shred it. Toss the shredded eggplant with 1 tsp kosher salt. Use your hands to squeeze out as much moisture as you can.
Discard the liquid and add the shredded eggplant to a bowl with the breadcrumbs, parmesan cheese, and egg. Use your hands to mix the ingredients together. The mixture should be moist, but not too soggy - add more bread crumbs if needed.
Arrange the provolone into a stack, then cut it into 12 cubes.
Divide the eggplant mixture into 12 equal portions. Form each portion into a ball. Use your thumb to make an indentation in each ball and tuck a portion of the provolone inside. Roll the balls to seal the provolone inside.
Place the eggplant balls on a baking sheet. Bake for 15 minutes, or until the bottoms have turned golden brown. Turn the eggplant balls and bake for an additional 10 minutes to brown the other side.
Serve with your favorite pasta sauce.