In a medium saucepan, combine the cooked rice, milk, sugar, cinnamon, and salt over medium heat.
Bring the mixture to a gentle simmer, stirring frequently to prevent sticking. Reduce heat to low.
Cook for 20-25 minutes, stirring occasionally, until the mixture thickens and becomes creamy. The rice should be soft and the pudding should coat the back of a spoon.
Remove from heat and stir in the butter and vanilla extract until the butter is completely melted.
Let the pudding rest for 5 minutes to thicken slightly. It will continue to thicken as it cools.
Serve warm in bowls, topped with fresh berries, raisins, a drizzle of honey, or sliced almonds. Add an extra sprinkle of cinnamon if desired.