Bring 1 1/2 cups water to a boil over high heat in a saucepan. Stir in your rice. Then, turn down the heat, cover the pan and let simmer for 20 minutes.
When the rice is done, put it in a clean saucepan with 1 1/2 cups milk, the sugar and salt. Cook this over medium heat, giving it a stir every once in awhile, until it thickens up and gets creamy, 15 to 20 minutes. Crack your egg into a small bowl and beat it with the remaining 1/2 cup milk. Slowly stir this mixture into the rice. Stir in your diced apricots and cook 2 minutes more. Take off the stove and stir in your butter, vanilla, orange zest, and cardamom. Grate some nutmeg over top.