Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the steaks with 1/2 teaspoon each salt and pepper. Cook to the desired doneness, 4 to 6 minutes per side for medium-rare. Remove from the skillet and let rest for at least 5 minutes before slicing.
Wipe out the skillet and heat the remaining tablespoon of oil over medium-high heat. Pat the chickpeas dry with paper towels and add them to the skillet. Cook, stirring occasionally, until slightly crispy, 3 to 5 minutes.
Stir in the tomatoes, cilantro, lemon juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Transfer to plates and sprinkle with the Feta. Serve with the steak.