How to Make It
Cover carrots with water in a large skillet. Bring to a boil over high; reduce heat to medium-high, cover and cook until carrots are tender, about 15 minutes.
Meanwhile, combine lemon zest, lemon juice, parsley, cilantro, pepper, garlic, ¼ cup of the oil, and ¼ teaspoon of the salt in a food processor (or mortar and pestle). Pulse (or grind) until pureed.
Drain carrots. Using a fork, mash with butter and ¼ teaspoon of salt.
Season steak with remaining salt. Heat remaining oil in a large skillet over high. Add steak; cook about 3 minutes per side for medium-rare. Let rest on a cutting board 5 minutes before slicing against the grain. Serve with carrots and parsley-cilantro puree.