Heat 1 tablespoon olive oil in a large 12-inch cast iron or stainless steel skillet over medium-high heat until shimmering. Meanwhile, toss 2 sliced medium zucchini, ½ teaspoon dried oregano, ½ teaspoon kosher salt, and ¼ teaspoon black pepper together in a large bowl until seasoned all over.
Working in batches if needed, arrange the zucchini in the skillet in a single layer. Cook until golden brown on the bottom, 4 to 5 minutes. Use a thin spatula or tongs to flip the zucchini. Cook until tender and browned on the second side, 3 to 4 minutes more.
Remove the skillet from the heat. Sprinkle the zucchini with 2 tablespoons finely grated Parmesan cheese if desired.
