½ cup plus 1 Tbsp extra-virgin olive oil
2 Tbsp coarsely chopped fresh rosemary
2 Tbsp balsamic vinegar
½ tsp kosher salt
¼ tsp freshly ground pepper
1-1pound beef rib-eye steak, trimmed of excess fat
¼ pound arugula, stemmed, washed, and dried
1 lemon, quartered lengthwise, optional
In a small saucepan, combine ½ 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 olive oil and half the salt and pepper. Cover tightly and shake vigorously. Set aside.
Preheat oven to 400 degrees F.
Season the rib eye steak with the remaining salt and pepper. Heat I Tbsp 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 to7 minutes for rare to medium-rare. Transfer to cutting board and let rest for 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 atop the arugula, drizzle with the reserved rosemary oil, and sprinkle with the reserved chopped rosemary. Serve with lemon quarters, if desired.