Place the cream cheese in a microwave-safe bowl and heat it for about 30 seconds, or until easy to stir. Stir it until creamy.
Add the milk, egg, egg yolk, mustard, salt, and pepper. Mix everything until the mixture is homogeneous.
In a separate bowl, add cooked rice. Then add cheese, ham, vegetables, and parsley. Stir everything.
Add the prepared cream to the rice mixture and stir until all the rice is coated.
Transfer the rice mixture to a 13"x9" (32x22cm) greased baking dish and cover it with cheese and oregano. Bake it at 350ºF (180ºC) for about 20 minutes, or until the food is hot and the cheese is melted.
Notes
You could add more mustard if you would like to have a more pronounced mustard flavor in this dish.