Combine the chard, onions and 1/2 cup water in a large pot. Bring to a simmer over high heat, then lower the heat to medium. Cover and cook, stirring frequently, until the chard is very tender, about 15 minutes.
Meanwhile, combine the cream cheese, nutmeg and 1/4 cup water in a medium saucepan. Place over medium heat and cook, whisking frequently, until the cheese melts and the mixture just bubbles around the edges. With a slotted spoon, add the cooked chard to the cheese mixture (discarding any excess liquid). Mix well and season with 1/4 teaspoon salt and some pepper. Garnish with the pine nuts. Set aside, covered, and keep warm.
Heat the oil in a medium skillet over medium heat. Sprinkle the steaks all over with 1/2 teaspoon salt and some pepper. When the oil is hot and shimmering, add the steaks and cook, turning once, until seared and rich mahogany, about 6 minutes per side. Transfer the steaks to a plate.
Add the garlic to the pan and cook, stirring occasionally, until aromatic, about 1 minute. Pull the skillet from the heat, add the vinegar, and use a wooden spoon to scrape up any browned bits that cling to the pan. Add in the butter, oregano and any juices from the steak. Stir until the butter melts.
Slice the meat against the grain into thin slices. Divide the steak evenly among four plates and pour the pan juices over. Divide the Swiss chard evenly among the four plates and serve each with a dinner roll and 1/2 cup of strawberries.