Heat olive oil in large skillet over MED-HIGH heat. Add mushrooms and onion, cooking about 5 minutes, until golden and soft. Season with 1/4 tsp salt and pepper, then stir in baby spinach until wilted.
Transfer mushroom mixture to plate and wipe out skillet. Crack eggs into small mixing bowl with 1 Tbsp water and remaining salt and pepper, and beat with small whisk or fork until blended and a little frothy.
Add 1 Tbsp of butter to skillet and heat over MED to MED-LOW. Add half of beaten egg mixture and stir them around the pan with a rubber spatula, pulling the sides in towards the middle, swirling the pan slightly so the runny egg mixture on top hits the pan and cooks. Cook about 2 minutes, until eggs are just slightly shiny on top.
Add half of mushroom mixture to one side of the omelet, then sprinkle with 1/4 cup cheese. Carefully lift up the edge of the omelet and check to see if the eggs are lightly golden on the bottom. Once they are, gently fold it over the filling.
Slide omelet out of skillet and onto plate to serve. Repeat steps 3 and 4 with remaining butter, egg mixture, mushroom mixture and cheese. Serve garnished with minced parsley and extra black pepper if desired.