In a large cast-iron skillet, heat 2 tablespoons olive oil over medium-high heat. Add the chard, season with salt and pepper, and cook for 5 minutes. Add the red peppers and the garlic to the skillet and cook for 5 minutes longer or until they are soft, stirring. Remove from the heat and set aside.

Add the eggs to a medium bowl. Season with salt and pepper and whisk until combined.

In a medium cast-iron skillet, heat the additional 2 tablespoons olive oil over medium-high heat. Pour the eggs into the skillet and cook for 4-5 minutes or until just set. Spoon the chard mixture evenly on one side of the omelet and fold the other side over.

Transfer the omelet to a serving plate. Serve immediately.