Break eggs into large bowl and whisk until the yolks are fully blended. Add salt and pepper. Heat 1 tablespoon butter in a 9 inch skillet and add chopped mushrooms, 1 tablespoon of water and a pinch of salt. Sauté over medium heat until water has evaporated. Add greens and cook until wilted, 1-2 minutes.
Turn heat to high, add remaining 2 tablespoons butter and pour egg mixture over mushrooms. Shake pan lightly to distribute mushroom evenly.
Cover pan and turn heat down to medium low. Allow to cook until the top of the frittata starts to bubble, about 3-4 minutes.
When frittata is opaque throughout (about 8 minutes total cooking time) remove from heat and invert the pan over a plate. Slice into eight pieces and serve hot.