Remove the steaks from the fridge and allow them to come to room temperature.
Preheat a lightly oiled grill (or grill pan) over high heat.
Season the steaks very generously on both sides with salt and pepper. Place them on the hot grill and cook for 3 minutes per side just to get some solid grill mark action. Transfer the steaks to a cooler part of the grill (or reduce the heat on your grill pan to medium) and cook for another 3 minutes or so per side for medium rare. Transfer the steaks to a cutting board and let them rest for 10 minutes to allow the juices to redistribute, then slice them thinly against the grain.
While the steak is resting, heat a large skillet over medium-high heat. When the oil is hot and shimmering, add the cherries and cook for about 3 minutes, shaking the pan occasionally, just until the fruit begins to soften. Add the balsamic and reduce the heat to medium. Cook for about a minute just until the balsamic has thickened slightly. Remove from the heat.
Add the arugula to a large bowl or serving platter. Toss the greens with a pinch of salt. Top with the red onion, steak, and cherry “dressing.” (You can toss the salad at this point if you like, but it’s prettier served in this form.) Sprinkle with cheese and add a few cranks of black pepper if you like. Serve immediately.