Clean the squash and cut into slices 1/4-inch thick. Combine in a small bowl and mix together the parsley, Italian seasoning, oregano, olive oil, vinegar, and pepper. Lightly coat the grill with cooking spray and preheat 5 minutes.
Place the squash in the grill, overlapping the slices, and cook for 6-8 minutes.
In a serving bowl, toss the squash gently with the Italian dressing and serve immediately.