Stir together butter, miso paste, and lemon zest in a medium bowl until combined. Let stand at room temperature at least 20 minutes. (Mixture can be made ahead and stored in an airtight container up to 2 weeks.)

Whisk together 3 tablespoons olive oil, vinegar, garlic, and ½ teaspoon salt in a small baking dish. Add steak, and turn to coat. Cover and refrigerate 1 to 4 hours, flipping steak once or twice to ensure even coverage.

Preheat oven to broil with oven rack 8 inches from heat source. Remove steak from marinade; discard marinade. Rub with 1 tablespoon lemon-miso butter. Place steak on a rimmed baking sheet lined with aluminum foil. Broil 6 minutes. Flip steak; broil 5 to 6 minutes for medium-rare (depending on thickness of the steak) or until a meat thermometer registers 130°F. Place steak on a cutting board. Dollop steak with 2 tablespoons lemon-miso butter. Let meat rest 10 minutes, then thinly slice the meat against the grain, and transfer to a serving platter.

While steak rests, heat oven to 425°F. Place bok choy in a large bowl, drizzle with remaining 2 tablespoons olive oil, and season with pepper and remaining ½ teaspoon salt; toss to coat. Arrange bok choy in a single layer, cut sides down, on hot baking sheet. Roast until stems are crisp-tender and leaves are browned and crisp at edges, 9 to 10 minutes. Transfer bok choy to platter with steak. Serve remaining lemon-miso butter on the side.