Old Fashioned Creamy Rice Pudding

1 ½ cups cooked rice

2 cups milk, divided

¼ teaspoon salt

⅔ cup golden raisins

1 egg, beaten

⅓ cup white sugar

1 tablespoon butter

½ teaspoon vanilla extract

Combine cooked rice, 1 1/2 cups milk, and salt in a saucepan over medium heat; cook and stir until thick and creamy, 15 to 20 minutes. Stir remaining 1/2 cup milk, golden raisins, beaten egg, and white sugar into the rice mixture; stirring continually. Continue cooking until egg is set, 2 to 3 minutes. Remove saucepan from heat; stir butter and vanilla extract into the pudding.