Prep the baking sheet: Arrange a rack in the middle of the oven and heat to to 375°F. Spray a rimmed baking pan with cooking spray. Line it with 2 layers of aluminum foil that fit neatly inside the rims, then place a sheet of parchment paper on top.

Prepare the fries: Prepare a large bowl filled with cold water. Stack several paper towels on top of one another and place them nearby. Peel and cut the potatoes into shoestring fries, about 1/4-inch by 1/8-inch by the length of the potato, adding them to the cold water as you work so they don't discolor. Remove the potatoes from water and transfer to the paper towels to dry. Discard the water from the bowl, wipe it dry, and then transfer the cut potatoes back into it. Add 2 tablespoons of the oil and gently toss to coat.

Par-bake the fries: Arrange the fries on the prepared baking sheet in a single layer. Bake without stirring or turning until the tip of a sharp knife pierces the fries without much resistance, 10 to 12 minutes. Wipe the potato bowl clean and set aside. While the fries bake, make the shallot butter and season the steaks.

Make the shallot butter: Place the butter into the reserved potato bowl. Peel and dice, mince, or grate the shallot and add to the bowl. Juice the lemon and add the juice to the bowl. Add the thyme and 1 teaspoon of the salt, then mash well to to fully combine; set aside.

Season the steaks: Place the steaks on the cutting board, and using the tip of a sharp knife, make 8 to 10 punctures in each. Cut off any visible gristle or silverskin, but leave on the flavor-rich fatty edge; set aside. Sprinkle both sides of the steaks with 2 teaspoons of the salt and the pepper. Place the steaks on a large plate, then wash and dry the cutting board.

Move the fries: Remove the fries from the oven and place the baking sheet on a heatproof surface. Increase the oven temperature to broil. With a flat spatula or tongs, carefully transfer the fries to the dry cutting board. Discard the parchment paper, leaving the aluminum foil layers. Pour 1/2 tablespoon of the oil onto the foil, just enough to coat it.

Broil the steaks: Place the steaks on the baking sheet. Broil for 4 minutes. Flip the steaks and broil about 4 minutes longer for rare (115 to 120°F), 5 to 6 minutes for medium-rare (120 to 125°F), and 6 to 7 minutes for medium (130 to 135°F). Timing will depend on the thickness of the steaks, so check on them early if you have thin steaks or prefer a more rare steak. If your steaks are different sizes or you desire a different doneness in each one, transfer each steak as they are ready to a serving plate.

Rest the steaks: Carefully remove the top aluminum foil layer from the sheet pan and pour any accumulated juices evenly over the steaks. Leave the last layer of foil on the pan. Top each hot steak with about 2 tablespoons of the butter mixture, tent each steak with a fresh piece of foil, and allow the meat to rest as the butter melts in. Meanwhile, finish the fries.

Finish the fries: Pour the remaining 2 1/2 tablespoons of oil onto the remaining sheet of foil on the baking sheet, and brush or tilt to coat. Return the fries to the baking sheet and arrange them in a single layer. Broil for 4 minutes. Turn them over using a spatula, or stir gently. Broil until they are as crisp and as browned you like, 2 to 4 minutes more. Sprinkle with the remaining 1 teaspoon of salt and serve with the steaks.