Cook the rice in the milk:
In a medium heavy-bottomed saucepan, bring the milk, rice, and salt to a boil over high heat. Reduce the heat to low and simmer partially covered until the rice is tender, about 20-25 minutes. Stir frequently to prevent the rice from sticking to the bottom of the pan.

Mix the egg and sugar, temper with the hot cooked rice:
In a small mixing bowl, whisk together egg and brown sugar until well mixed. Add a half cup of the hot rice mixture to the egg mixture, a tablespoon at a time, vigorously whisking to incorporate.

Add the egg mixture back to the pan:
Add egg mixture back into the saucepan of rice and milk. Reduce the heat to low and stir until thickened, or about 160°F (71°C).

Be careful not to have the mixture come to a boil at this point or it will curdle. Remove from heat and stir in the vanilla, raisins, and cinnamon. The pudding will thicken as it cools; when it is warm, it will be a bit on the runny side.

Serve warm or cold.