Prepare the Vinaigrette: In a small bowl or jar, whisk together the olive oil, lemon juice, Dijon mustard, dried oregano, minced garlic, salt, and pepper until well emulsified. Set aside.

Prepare the Zucchini for Grilling: Lightly brush both sides of the zucchini planks with a small amount of olive oil (not included in the ingredient list above, assume standard cooking oil) and season lightly with salt and pepper.

Grill the Zucchini: Preheat a grill or grill pan to medium-high heat. Place the zucchini planks on the hot grill and cook for 3-4 minutes per side, until tender and distinct grill marks appear. Remove from heat and let cool slightly.

Assemble the Salad Base: Once the grilled zucchini is cool enough to handle, chop it into bite-sized, 1-inch pieces. In a large mixing bowl, combine the chopped grilled zucchini, halved cherry tomatoes, and thinly sliced red onion.

Dress and Finish: Pour about half of the prepared lemon vinaigrette over the zucchini mixture and gently toss to coat. Add the torn fresh basil leaves and gently fold them in.

Serve: Transfer the salad to a serving platter or individual bowls. Drizzle with more vinaigrette to taste, and sprinkle the crumbled feta cheese over the top before serving immediately.