In a large saucepan, combine cooked rice, milk, beaten egg, sugar, and salt. Bring the mixture to a vigorous simmer over medium heat stirring frequently with a rubber spatula or wooden spoon so the pudding doesn’t stick, and the egg doesn’t scramble.
Reduce heat to maintain a bare simmer, stirring frequently until thick and creamy about 10-12 minutes.
Remove from heat. Stir in vanilla, butter, and raisins. Pour into a serving bowl or individual bowls. Cover the pudding with plastic wrap to prevent skin from forming on the top. Refrigerate until ready to serve.
Serve warm or cold topped with whipped cream and a sprinkling of cinnamon.
Notes
The rice pudding will continue to thicken as it cools. Thin out with more milk if desired.