In a large nonstick skillet, heat 1 tablespoon of olive oil and 1 tablespoon of unsalted butter over medium-low heat. Add the thinly sliced onion if you're using it, and cook gently for about 10 to 11 minutes until golden brown.

Once the onions are ready, add the sliced zucchini, salt, black pepper, and dried thyme. Toss gently and let cook for about 1 minute.

Increase heat to medium and continue to cook the zucchini mixture for about 10 to 15 minutes until just tender and slightly browned.

Sprinkle ¼ cup of Parmesan cheese over the top, allow it to melt and stir gently to combine before serving.