Preheat a grill to medium high. Season the steak with salt and pepper and rub with 1 tablespoon olive oil. Lightly brush the grill grates with olive oil. Grill the steak 6 to 8 minutes per side for medium rare. Transfer to a cutting board to rest, about 10 minutes.
Meanwhile, make the pesto: Puree the remaining 4 tablespoons olive oil, 1 tablespoon lemon juice, the cilantro, garlic, cumin, paprika, 3 tablespoons water and 1/2 teaspoon salt in a mini food processor or blender until smooth.
Toss the chickpeas, carrots, scallions, the remaining 1 tablespoon lemon juice and 3 tablespoons of the pesto in a medium bowl; season with salt and pepper. Thinly slice the steak against the grain. Serve with the chickpea salad and the remaining pesto.