Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Season the steaks with salt and pepper, and sear them in the hot pan (working in batches if need be) until the steaks have a nice crust on the outside, about 3 minutes per side.
While the steaks are cooking, toss the mozzarella, tomatoes and basil together in a mixing bowl. Drizzle with the remaining 2 tablespoons EVOO and season with salt and pepper. Serve the steaks topped with the caprese salad and a fresh green salad alongside.