Crack both eggs into a mixing bowl. Whisk the eggs until completely combined, and season with salt and pepper.
In an 8-inch skillet over medium heat, add just enough oil to cover the bottom of the pan. Add onion, turmeric, cayenne, and mushrooms. Cook for 5 minutes, stirring occasionally.
Add the chard, and cook another 2 minutes or so, until chard is wilted.
Pour the eggs into the skillet. Immediately tilt the pan so the eggs coat the entire bottom, and mix in with the veggies. Season with a pinch of salt and pepper. Stir occasionally, until eggs are completely cooked through, about 3-4 minutes or so.
Remove to a plate. Taste and add additional salt or pepper as needed.