Wash the zucchinis and trim the ends. Slice them lengthwise into thin strips, about 1/4 inch thick.
Lightly drizzle or brush the zucchini slices with olive oil. Heat a grill or grill pan over medium-high heat and grill the zucchini for 2–3 minutes on each side, until tender and grill marks appear.
In a small bowl, combine extra virgin olive oil, minced garlic, dried oregano, and salt. Mix well.
Place the grilled zucchini in a serving dish. Pour the garlic-oregano dressing over the warm zucchini slices and gently toss to coat.
Sprinkle with chopped fresh parsley before serving.