In a shallow dish, combine vinegar, 1/4 cup EVOO, garlic, marjoram or oregano, cilantro and cumin.
Pat steaks dry, season with salt and pepper and give them a turn in the marinade. Let marinate 4 hours in the fridge.
Heat a skillet over medium heat with 2 tablespoons EVOO. Add onions, season with salt and pepper and cook until tender, about 20 minutes. Deglaze the pan with the beer or chicken stock. As onions cook, take the meat out of the fridge to bring it back up to room temperature before cooking.
When onions are just about tender, heat a cast-iron skillet over medium-high to high heat. Shake excess marinade off the steaks and cook in batches in the hot pan until crispy, 2 minutes on each side. Keep finished steaks on warm platter while you finish the rest of the pieces. When all the steaks are cooked, turn off heat, add butter to the pan and melt. Stir in parsley and lime juice.
Serve steak immediately topped with onions and the lime butter, with black beans and rice alongside.