In a saucepan over medium-high heat, mix the rice, milk, and salt. Cook until it starts to thicken (for around 15-20 minutes) while stirring often to prevent the rice from burning. Add the sugar and stir until melted.

Take about ¼ cup of the hot rice mixture and rapidly mix it into the beaten eggs. Once tempered, add to the hot pudding and rapidly whisk them in. Cook for a few more minutes, stirring constantly until it thickens.

Remove the pudding from the heat and stir in the butter and vanilla extract. Season with cinnamon to taste.

Serve rice pudding warm or cold. Enjoy!