Preheat the grill to medium-high heat, giving it about 5 minutes to reach temperature. Lightly drizzle the onion slices with olive oil and season with kosher salt. Generously season both sides of the ribeye with salt and freshly ground black pepper.
Place the onions on the grill and cook for 2 to 3 minutes per side until they develop visible grill marks and soften slightly. Grill the steak, turning occasionally, until it reaches your preferred doneness — about 6 minutes per side for medium-rare, or until an instant-read thermometer registers 130°F when inserted into the thickest part.
Once grilled, transfer the steak and onions to a cutting board and let them rest for several minutes. Slice the steak thinly against the grain for tenderness.