Half-fill a skillet with hot water that is slightly larger than the one in which the eggs will cook.
Bring it to a boil over high heat, then reduce the heat to maintain a low simmer.
In a small bowl, lightly beat the eggs, milk, salt, and pepper.
Heat the olive oil in a small skillet over high heat.
Add the chopped mushrooms and cook for about 1 minute.
Stir in the finely chopped parsley and cook for a few seconds, then remove the skillet from the heat.
Add the beaten egg mixture and place the skillet in the larger skillet filled with hot water.
Stir constantly with a wooden spoon until the eggs are set but still soft.
You can prepare this ahead if desired.
Spoon the mixture onto each bread slice.