In a medium bowl, whisk together the eggs, milk, salt, and pepper until the mixture is homogeneous and no streaks of egg white remain.
Place a non-stick skillet over medium heat and melt half of the butter.
Add the sliced mushrooms to the skillet and sauté for 4 to 5 minutes until they are golden brown and their moisture has evaporated.
Add the baby spinach to the skillet and toss for 1 minute until just wilted. Remove the mushrooms and spinach from the skillet and set aside on a plate.
Wipe the skillet clean with a paper towel and return to medium-low heat. Melt the remaining butter.
Pour the egg mixture into the skillet. Let the eggs sit undisturbed for 20 seconds until the edges begin to set.
Using a heat-resistant silicone spatula, gently push the eggs from the edges toward the center to create soft curds.
When the eggs are nearly set but still look slightly moist, fold the cooked mushrooms and spinach back into the eggs.
Sprinkle with parmesan cheese, remove from the heat immediately, and serve.