Place softened cream cheese, crab meat, salt and pepper into a small mixing bowl. Stir to combine; set aside.
In small omelet pan or frying pan over medium heat, melt 1/2 Tablespoon of butter. Add mushrooms and onion and saute, stirring occasionally, until softened, about 2-3 minutes.
Meanwhile, whisk together egg and milk in a small bowl and set aside.
Transfer cooked mushroom mixture into bowl with crab and cream cheese, then carefully clean the inside of the omelet pan with paper toweling. Place pan back onto medium heat and add remaining butter to melt.
Pour egg mixture into pan and cook until edges are set and the center has started to set up, about 3 minutes. Place crab mixture evenly down center of omelette. Gently slide a spatula under outside third of omelette and carefully fold it over the crab mixture. Use spatula to fold remaining third over the egg you just folded so that the filling is contained inside of the omelette.
Use your spatula to flip entire omelette over and cook for another 1-2 minutes, until egg has completed cooking.