Heat a large skillet or cast-iron pan over medium-high heat. Add half the butter, then add the ground beef and cook until it’s browned, breaking it up with a spoon as it cooks.
Season with a pinch of salt and pepper, then add the dried thyme, oregano, cumin, and paprika. Transfer the beef to a bowl and set it aside.
Add the onion to the pan and cook until it softens, about 5 minutes. Stir in the mashed garlic and cook for another minute.
Add the diced potatoes and cook for 5–6 minutes, giving them a stir now and then, until they’re golden and starting to get tender. (Cover the pan with a lid to speed things up.) Pour in the water or broth and let everything cook for another 10–12 minutes, or until the potatoes are fully tender.
Return the cooked beef to the skillet and let it all cook together for another 4 minutes, just until everything is heated through.
Garnish with parsley or green onions.
Serve hot on its own, or add a simple salad or some crusty bread on the side.