Preparation

• Pat the steak dry, and season with 1-1/4 tsp. salt and 1/2 tsp. pepper.
• In a stand blender (or using a hand-held immersion blender), purée the broth, tomatoes, and vinegar.
• Put a large, heavy-based stainless-steel skillet over medium-high heat for 1-1/2 minutes (it’s ready when a droplet of water instantly evaporates upon hitting the surface). Add 2 Tbs. of the oil. Once it’s shimmering hot, about 30 seconds, carefully add the steaks, evenly spaced.
• Cook the steaks, undisturbed, until brown around the edges and a corner easily pulls up when lifted with tongs, about 3 minutes. Flip and cook the other side until medium rare, 2 to 3 minutes more; if checked with an instant-read thermometer, a thicker piece will register 130°F to 140°F and the steak will be bright pink when sliced. Transfer to a cutting board, and tent with foil. Rest for at least 10 minutes while you make the sauce.
• Return the skillet to the stovetop, and lower the heat to medium. Add the remaining 1 Tbs. of the oil and the garlic, and cook, stirring, until the garlic sizzles and becomes fragrant, about 30 seconds. Add the thyme, pimenton, and saffron, and cook, stirring, for 15 seconds. Add the tomato purée. Bring to a boil, and then reduce to a simmer. Cook, stirring occasionally, until reduced by about half, about 5 minutes. Stir in the capers and parsley, and season with 1/8 tsp. salt and 1/8 tsp. pepper.
• Spoon over the steak and serve immediately. Garnish with fresh thyme sprigs.