Caramelize the onions: In a skillet over medium heat, melt 1 tbsp butter and add the sliced onions. Cook, stirring occasionally, for 20-25 minutes until soft and golden brown. Remove and set aside.
Prepare the mashed potatoes: While the onions cook, boil the potatoes in salted water until fork-tender (about 15 minutes). Drain, then mash with warm milk, butter, salt, and pepper. Keep warm.
Cook the ribeye steaks: Season steaks generously with salt and pepper. Heat olive oil in a skillet over high heat. Sear the steaks for 3-4 minutes per side, depending on your preferred doneness. Remove steaks from the pan and let them rest.
Optional sauce: Deglaze the pan with beef broth, scraping up the browned bits, then reduce slightly to make a quick pan sauce.
Assemble: Place a scoop of mashed potatoes on each plate, top with a ribeye steak, and finish with caramelized onions.