Prepare the Zucchini
Clean and dry the zucchini, then use a sharp knife or a vegetable peeler to carefully cut each one lengthways into thin strips.
Make the slices thin enough to roll them up but not so thin that they tear.
Make the cheese filling.
Take the mozzarella that has been shredded, the Parmesan cheese, the minced garlic, the Italian seasoning, the oregano, the black pepper, and half of the fresh parsley and put them all into a bowl.
Combine all of them until they are evenly mixed.
Season the Zucchini
Place the slices of zucchini flat on a clean cutting board or tray.
Apply a little olive oil to both sides and then season with a small quantity of salt and black pepper.
Fill and Roll
Put a little of the cheese mixture close to one end of each zucchini slice.
Take the zucchini and roll it up tightly around the filling. Keep doing this until all of the zucchini slices and the cheese mixture have been used.
Make sure not to fill the rolls too full so that the cheese remains inside when grilling.
Cook the zucchini rolls on a grill.
Turn the grill pan or outdoor grill to medium heat first.
Brush the grill with a small amount of olive oil and lay the zucchini rolls with the seam side down.
Cook the grill for about 2 to 3 minutes on each side, making sure to turn them over as they are cooking.
Keep grilling the zucchini until it is tender, golden in colour and has nice grill marks; the cheese should have melted and be deliciously soft and stretchy.
Finish and Serve
Place the grilled zucchini rolls on a serving plate.
Add some fresh parsley and, if you like, a bit of extra Parmesan cheese or red pepper flakes.
Serve it right away since the cheese is still warm and melted.