Heat a large cast-iron skillet over medium heat. Add the olive oil and 2 tablespoons of ghee.
Once the ghee has melted, add the cubed potatoes to the skillet. Sprinkle with garlic, thyme, oregano, salt, and pepper.
Cook the potatoes for 2-3 minutes without stirring to allow them to brown. Stir every 1-2 minutes, cooking until the potatoes are golden brown and fork-tender, about 8-10 minutes.
Note: If the potatoes are crowded or cut into larger pieces, they may take longer to cook.
Remove the potatoes from the pan and set aside.
Increase the heat to medium-high and add the remaining 2 tablespoons of ghee to the skillet.
Once the ghee has melted, add the steak cubes and season with a dash of salt and pepper.
Let the steak cook undisturbed for at least 2 minutes to develop a crust. Stir the steak pieces and cook for another 1-2 minutes until browned and cooked to your desired doneness.
Return the cooked potatoes to the skillet and stir to combine. Taste and adjust seasoning with additional salt and pepper, if needed.
Garnish with freshly chopped parsley and serve immediately.