In a medium saucepan over medium heat, combine the cooked rice and milk. Stir gently to break up any clumps.

Add the granulated sugar and a pinch of salt. Continue stirring until the mixture begins to simmer.

Whisk the egg in a small bowl. Slowly pour a ladle of the hot rice mixture into the egg, whisking constantly to temper.

Pour the egg mixture back into the saucepan and cook for 2–3 minutes, stirring continuously, until the pudding thickens.

Remove from heat and stir in the butter and vanilla extract until fully incorporated.

Transfer to serving dishes and let cool slightly. Sprinkle with cinnamon and optional raisins.