Brush the steak with a bit of olive oil and sprinkle generously with salt and pepper. Grill the steak in a grill pan or outside on your grill if the weather permits. If you prefer your steak medium rare, it will only take 3 - 5 minutes per side depending on the thickness of your cut of steak.
Spread the arugula on your serving platter. Salt and pepper it to your liking. If you are using tomatoes, cut those up and display around the edges of the platter.
Once your steak is cooked to your desired doneness, remove it from the pan and let it rest for at least 5 minutes to allow the juices to remain in the meat. If you slice it right away, you’ll lose all the juices onto the cutting board.
While your steak is resting, drizzle olive oil and balsamic all over arugula. Next, spread your fresh parmesan shavings all over and then a squeeze of lemon juice if you like. Slice the steak across the grain and display down the center of the bed of arugula. Add a bit more salt and pepper, olive oil, balsamic, and parmesan if you’d like.