To make the steaks: Bring the rib eyes to room temperature for a minimum of 30 minutes.
Meanwhile, in a spice grinder or mortar and pestle, coarsely grind the black, pink, and green peppercorns. Transfer them to a bowl and whisk them together with the brown sugar and cinnamon. Sprinkle this spice rub on a plate, place a rib eye on top of the rub and gently press down so it adheres. Flip the steak and repeat. Repeat with the other steak. Just before cooking, sprinkle both sides of the steaks with the salt.
To cook the steaks on the stove, preheat the oven to 350℉. Preheat a cast-iron skillet over high heat. When slightly smoking, drizzle with olive oil. Depending on the size of your skillet you may want to cook one steak at a time. Sear the steaks on one side for 3 to 4 minutes, undisturbed, to create a crust on the steaks. Flip and sear the other side. Place the skillet in the preheated oven and cook about another 10 minutes for medium-rare or 20 minutes for medium-well. Remove from the oven and let rest for 10 minutes before slicing.
To grill the steaks, preheat a grill to high. Sear both sides of the steaks for 2 to 4 minutes. Reduce the heat to medium and continue to grill for about 8 more minutes for rare, 12 more minutes for medium-rare, 15 more minutes for medium, and 18 more minutes for well done. Remove from the grill and let rest for 10 minutes before slicing.
To make the salad: Just before serving, in a large bowl, combine the arugula, lemon juice, oil, and salt. Toss until coated. Don’t do this too early or the arugula will get soggy.
Serve the sliced steak with arugula on the side and top with shavings of Parmigiano-Reggiano.
Abner Ramirez and Amanda Sudano Ramirez are LA-based singer-songwriters and parents of three who love to collaborate, bond, and have fun together in the kitchen. The duo embraces the joys and challenges of cooking while juggling family life.