Slice the zucchinis lengthwise into very thin slices (about 1/8"); the use of a mandoline is very strongly recommended.
Place the slices on a large baking sheet and drizzle with a little bit of olive oil, then sprinkle them generously with salt and pepper. Let the slices sit for about 5 minutes; this will make them more pliable.
Delicately thread the slices onto wooden skewers - 3 slices per skewer - alternating between colors if using yellow and green zucchinis.
Place the skewers on the hot grill and grill for 1-2 minutes, just enough to soften the zukes and get nice grill marks on them, then very delicately flip the skewers with a pair of tongs and continue grilling for another minute or so.
Remove to a plate and garnish with chopped parsley and Parmesan cheese, if desired, before serving.