Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
For the sticky barbecue onions: Heat a cast-iron skillet over direct heat. Melt the butter. Add the onions with a pinch of salt and cook until they begin to caramelize, about 5 minutes. Whisk together the ketchup, vinegar, mustard, sugar, cayenne, cumin and paprika in a small bowl (see Cook's Note). Add the sauce to the onions. Season with salt and pepper. Bring to a simmer and cook until the liquid reduces and begins to get sticky, 8 to 10 minutes. Move over indirect heat to keep warm while you cook your steak.
For the steak: Sprinkle the steak with salt and pepper on both sides and bring to room temperature. Drizzle the steak with the oil and sprinkle with the oregano and paprika on both sides. Place the steak over direct heat and cook until it gets a nice char, 3 to 5 minutes per side for medium-rare.
Add a splash of oil, a pinch of salt and some pepper to a cutting board. Place the steak on the seasoned oil on the cutting board, flip and rest 5 minutes. Slice the steak against the grain and serve topped with the onions.
(Alternatively, you can cook the onions over medium-high heat on a stovetop, and the steak in a grill pan or cast-iron skillet over high heat on a stovetop.)
Substitute 3 teaspoons of your favorite dry barbecue rub in place of the cayenne, ground cumin and sweet paprika.
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