Place rice, sugar, mild and cardamom in a 3-qt stainless sauce pan and place over a medium burner. Bring to a boil and simmer until rice is tender, about 18 - 20 minutes, stirring occasionally.
Combine cream, eggs, yolks and salt in a mixing bowl and whisk together. Ladle one cup of hot cooked rice into egg mixture and whisk together to temper. Add tempered egg mixture back to saucepan and carefully bring to a boil stirring continually.
Transfer to a ceramic or glass container and lay plastic wrap directly onto the top of the pudding to prevent a skin from forming while the pudding cools. Serve chilled and store in refrigerator.