In a saucepan, combine 1/2 cup olive oil with the rosemary. Bring to a simmer over low heat and remove from the heat. Let rest 10 minutes. Strain through a sieve, reserving both the infused oil and the chopped rosemary. In a small jar, combine the balsamic vinegar with the reserved rosemary oil and half the salt and the pepper. Cover tightly and shake vigorously. Set aside. Preheat oven to 400 degrees. Season the rib steak with the remaining salt and pepper. Heat 1 tablespoon olive oil in a medium ovenproof skillet over high heat. Sear the steak 2 to 3 minutes. Turn the steak over and place the pan in the oven. Cook for an additional 5 to 7 minutes for rare to medium-rare. Transfer the steak to a cutting board and let rest 4 to 5 minutes. Arrange the arugula on a serving platter. With a long sharp knife, cut the steak on the bias into thin slices. Arrange the slices on top of the arugula, drizzle with the reserved rosemary oil and sprinkle with the reserved chopped rosemary. Serve with the lemon quarters.