In a large mixing bowl, combine the sliced potatoes and onions. Drizzle with olive oil and melted butter, ensuring each slice is coated. Sprinkle with garlic, thyme, salt, and pepper.
Toss the mixture gently to ensure even distribution of seasoning.
Transfer the mixture to a large baking dish or a sheet pan. Spread it out in an even layer.
Roast in the preheated oven for 35-40 minutes, stirring halfway through, until the potatoes are tender and golden brown.
If using, sprinkle the Parmesan cheese over the potatoes during the last 5 minutes of cooking.
Once out of the oven, let the dish rest for a few minutes. Garnish with chopped parsley before serving.