Line a rimmed baking sheet with parchment paper and then lay an oven-safe cooling rack over the parchment paper. Rub the cooling rack with ½ the olive oil to coat and then set aside.
In a small bowl, combine the parmesan, thyme, oregano, garlic powder, kosher salt, and pepper.
Place the sliced zucchini and squash in a medium mixing bowl and drizzle the remaining ½ tbsp. olive oil over. Toss to coat evenly.