Heat a large cast-iron skillet over medium-high heat. When it?s hot, add the oil. Sprinkle the steaks with salt and pepper and cook 2 steaks until browned on one side, about 4 minutes. Remove the steaks from the skillet. Add the 2 remaining steaks and cook until browned on one side, about 4 minutes. Flip these steaks and return the first 2 steaks to the skillet, raw-side down. Add 2 tablespoons of the butter and the thyme. Once the butter melts, tilt the skillet slightly to pool the liquid, then constantly spoon the butter over the steaks until the meat is medium-rare, about 4 minutes more. Transfer the steaks to a rimmed plate to rest, reserving the skillet.
Add the pasta to the boiling water and cook according to package directions. Reserve 1/4 cup of the cooking water and drain the pasta. Return the pasta to the pot and toss with 2 tablespoons of the butter and the parsley.
Put the tomatoes in the same skillet used to cook the steaks and cook over medium heat until blackened in spots and softened, about 4 minutes. When the tomatoes are very soft, remove the thyme sprigs and carefully mash the tomatoes with a slotted spoon or potato masher. Stir in the remaining 2 tablespoons butter and the vinegar until incorporated, adding up to 1/4 cup pasta cooking water if necessary to make a smooth sauce. Season with 1/2 teaspoon salt.
Slice the steaks thinly against the grain and add any juices that accumulate to the tomato butter sauce. Divide the sliced steak among 4 plates and spoon some tomato butter sauce over the top. Serve with the noodles.
Copyright 2016 Television Food Network, G.P. All rights reserved.