Season the beef with salt and pepper and let come to room temperature. Heat a large cast-iron skillet or griddle over medium-high. Drizzle the steaks with a little oil.
In a second skillet with a lid, heat the oil, four turns of the pan, over medium-high. Add the anchovies and cook, stirring occasionally, until they melt into the oil, about 2 minutes. Add the garlic and chile and cook, stirring often, until fragrant, 1 to 2 minutes. Add the tomatoes, cover the pan, and cook, shaking the pan occasionally, until the tomatoes burst, 3 to 4 minutes. Using the back of a spoon, mash the tomatoes a bit. Stir in the beans, parsley, capers, basil and olives. Cook, stirring often, until heated through, 1 to 2 minutes. Cover and remove from the heat.
Add the steaks to the preheated skillet and cook, turning once, about 5 minutes for medium-rare and 7 minutes for medium-well. Drizzle the steaks with Worcestershire.
Divide the tomato-bean mixture among plates. Top with the steaks.