In heavy saucepan cook milk and salt over medium heat until warm. Stir in rice and continue cooking over medium heat until mixture comes to a boil.  Reduce heat and simmer gently for 20 minutes, stirring occasionally.  Add 1/4 cup evaporated milk and simmer 2 minutes, stirring frequently.

Combine eggs, sugar, vanilla, and remaining 3/4 cup evaporated milk in bowl. Stir about 1/2 cup of the hot rice mixture into the egg mixture. Then, stir the egg mixture into the rice mixture in the saucepan and cook over low heat until mixture thickens slightly, stirring frequently.  The mixture should come just to a boil. Remove from heat immediately.  Do not continue to boil or the mixture will curdle.