Follow the steps in order for the best result.
In a saucepan, bring 2 cups of water to a rolling boil. Add the rice, then reduce the heat to low. Cover the pot and let it simmer for approximately 20 minutes, stirring from time to time, until the water has been fully absorbed by the rice.
Introduce the fat-free half-and-half, brown sugar, cinnamon, and kosher salt to the cooked rice. Mix well. Set the heat to medium and cook, stirring frequently to prevent any sticking or clumping. Continue this process for about 15 minutes, or until the mixture thickens into a creamy consistency.
Incorporate the beaten egg into the mixture, stirring continuously. Cook for an additional 5 minutes, ensuring it's well combined.
Remove the saucepan from the heat. Gently stir in the light butter and vanilla extract until they are fully incorporated into the rice pudding.