In a medium saucepan, combine milk, sugar, cream, vanilla bean with scraped seeds, vanilla extract, salt, cinnamon, nutmeg, and cardamom. Bring mixture to a boil; remove from heat. Remove 2 cups mixture; set aside. Steep remaining mixture, covered, for 30 minutes.

In a small saucepan, bring water to a boil. Add rice, cooking for 2 minutes. Drain rice. Add rice to steeped milk mixture. Cook, covered, over medium-low heat until liquid is mostly absorbed, approximately 45 minutes, stirring occasionally.

In a small bowl, whisk together egg yolks and reserved 2 cups milk mixture. Add to rice mixture, stirring well. Cook over medium heat until thickened, 10 to 15 minutes, stirring constantly. Do not allow mixture to boil.

Add butter, stirring until melted. Remove from heat, transfer to a bowl, and cool slightly. Serve immediately.

Garnish with nutmeg and cinnamon, if desired. Store in an airtight container in refrigerator for up to 3 days.