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In a small nonstick pan over medium heat, add the remaining 2 tablespoons butter and cook until the butter begins to shimmer. Whisk the eggs in a bowl until light and fluffy and sprinkle with salt and pepper. Pour the eggs into the pan and let the eggs cook until the bottom starts to set, up to a minute. With a heat-resistant rubber spatula, gently push one edge of the egg into the center of the pan while tilting the pan to allow the liquid egg to flow in underneath. Repeat with the other edges, until there's no liquid left. Place the greens down the center of the omelet and roll into a cylinder. Remove to a platter, season the top with salt and pepper and top with the parsley.