For the salsa roja: Add the tomatoes, garlic, jalapeno and onion to a medium saucepan. Add 6 cups water and bring to a boil over high heat. Simmer until the vegetables are softened, 15 to 20 minutes.
Drain the vegetables, add to a blender and blend until smooth. Transfer to a bowl and stir in the vinegar. Season with salt and pepper. Let cool, then cover with plastic wrap and refrigerate until ready to serve.
For the chimichurri: Add the vinegar, garlic and a generous pinch of salt to a blender and blend on low until smooth. Add the parsley, cilantro, ice, oregano and jalapeno and blend on medium speed. With the blender running, slowly drizzle in the olive oil and blend, stopping to scrape down the sides if necessary, until smooth, about 1 minute. Season with salt and pepper. Transfer the chimichurri to a serving bowl, cover with plastic wrap and refrigerate until ready to serve.
For the steak: Let the steak sit at room temperature for about 30 minutes before cooking.
Position an oven rack 5 to 6 inches from the broiler and preheat the broiler.
Heat a large cast-iron skillet over medium-high heat. Pat the steak dry and sprinkle generously with salt and pepper; the steak should be almost completely white from the salt. Add the oil to the hot skillet and when it begins to smoke, add the steak. Cook the steak until browned and crusty on both sides, about 4 minutes per side. Remove to a cutting board.
Cut the strip steak from the bone and carve the meat across the grain. Cut the tenderloin filet from the bone and carve the meat across the grain. Place the bone back in the center of the skillet and arrange the sliced steak around the bone in its original formation so that it looks like a full steak. Top with the butter, garlic and thyme.
Broil until the butter is melted and a thermometer inserted sideways in the center of the steak registers 120 degrees F for medium rare, 3 to 4 minutes (see Cook’s Note). Tilt the skillet slightly to pool the butter, then spoon it over the steak several times to coat.
Transfer the steak to a serving platter and pour the melted butter over top. Top one half of the steak with the chimichurri and spread evenly. Top the other half with the salsa roja and spread evenly. Serve with the remaining chimichurri and salsa roja on the side.