If you don't have leftover cooked cabbage, bring a pot of salted water to a boil. Add sliced cabbage and cook for 3-5 minutes until tender. Drain thoroughly and let cool.
In a large mixing bowl, combine the cold mashed potatoes, cooked cabbage, and any other leftover vegetables you're using.
Add the finely diced onion, salt, pepper, and dried thyme if using. Mix everything together well.
Heat a large non-stick skillet or cast iron pan over medium heat. Add the butter and oil.
Once the butter has melted and is bubbling, add the potato-vegetable mixture to the pan. Press down with a spatula to form an even cake that covers the bottom of the pan.
Cook undisturbed for 8-10 minutes until the bottom develops a golden brown crust.
Either flip the cake in one piece (if you're feeling confident) or break it into sections to flip more easily. Continue cooking for another 6-8 minutes until the other side is also golden and crispy.
Sprinkle with fresh parsley if desired and serve hot.