In a large, heavy-bottomed saucepan, combine the rice, 3 cups of the milk, sugar, salt, cinnamon, and nutmeg. Bring to a gentle simmer over medium heat, stirring occasionally to prevent sticking.
Reduce the heat to low and cook for 25-30 minutes, stirring frequently, until the rice is tender and the mixture is thick and creamy.
In a small bowl, whisk together the remaining 1 cup of milk and the eggs until well blended.
Gradually add the egg mixture to the saucepan, stirring constantly to incorporate. Continue cooking for 5-7 minutes, or until the pudding thickens further.
Remove from heat and stir in the butter, vanilla extract, and raisins (if using).
Let the pudding cool slightly before serving. Sprinkle with additional ground cinnamon on top and enjoy warm or chilled.
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