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Step 1
Cook the potatoes: Heat the oil in a 12-inch cast iron skillet over medium heat until shimmering. Add the potatoes cut-side down, sprinkle with the salt, and cook undisturbed until golden-brown and the potatoes release easily from the pan, about 10 minutes. Using tongs, flip each wedge to another cut side and cook until browned and the potatoes are tender, 10 to 15 minutes more.
Step 2
Meanwhile, dry the steaks with paper towels. Season all over with 1 teaspoon salt and set aside. When the potatoes are ready, transfer to a serving platter.
Step 3
Cook the steaks: Wipe out the skillet with paper towels and return to high heat until the pan starts to smoke just a bit. Carefully place the steaks in the hot pan and cook on the first side until enough of a crust has developed that the steaks no longer stick to the pan, about 1 minute. Flip and cook on the other side for 1 minute. Continue cooking and flipping for a total of 4 minutes.
Step 4
Carefully add the butter to the pan. Flip the steaks once more. Tilt the pan so the butter pools on one side and add the garlic to the pool. Use a large spoon to baste the butter over the steaks. Flip again and repeat with basting. Continue cooking and begin checking the internal temperature of the steaks at 6 minutes total cook time for your preferred doneness. Medium rare is between 125°F and 130°F. Remove the pan from the heat.
Step 5
Transfer the steaks to a clean cutting board and let rest for 5 minutes. Meanwhile, stir the parsley and lemon juice into the juices in the pan. Let cool for a few minutes, then taste and season with more salt and lemon juice as needed.
Step 6
Cut the steaks across the grain into 1/2-inch-thick slices. Place on top of the potatoes and drizzle with the garlic butter pan sauce.