Place potatoes in a large pot and cover with cold water. Season heavily with salt. Bring to a boil over high heat then reduce to a simmer cooking potatoes until done. Approximately 20 minutes. Drain potatoes.
Preheat oven to 400 degrees.
Heat oil and butter in a cast iron skillet until better is melted. Add potatoes to skillet. Using a potato masher or large fork, smash each potato until skin is broken.
Sprinkle potatoes with thyme, salt and pepper.
Place skillet in oven. Cook potatoes until a crispy edge forms around the pan, about 8 minutes. Remove from oven. Sprinkle on parmesan cheese and return to oven for an additional 8 to 10 minutes or until potatoes are crunchy on top.
Remove skillet from oven. Sprinkle with fresh parsley and serve.