Chop the mushrooms, onion and garlic. Saute with butter in a frying pan over medium heat. While this cooks, chop the chard. Add to the pan after mushrooms are soft, after 5 to 7 minutes. Cook, stirring well for 3 minutes, until greens are soft and bright.
In a medium mixing bowl, whisk the eggs. Add the cheese. Season with salt and pepper. Stir well to combine.
Add in the sauteed veggies to the eggs. Mix well and pour into a greased 8 by 8-inch baking dish.
Bake for 25 to 30 minutes, until top is golden brown and the center is set.