Preheat a gas or charcoal grill over high heat.
Whisk together the butter, cheddar cheese, basil and oregano, then season with salt and pepper to taste.
Place the courgettes on a sheet of foil. Spoon butter mixture over zucchini. Bring up foil sides. Double fold top and ends to seal packet, leaving room for heat circulation inside.
Place foil packets on the grill and cook until just cooked through, which is about 15-20 minutes.
Garnish with red pepper flakes and parsley, if desired and serve immediately.