In a small saucepan set over medium-low heat, combine the cooked white rice, whole milk, and salt. Stir occasionally and allow the mixture to simmer gently until it begins to thicken slightly—this should take around 10 minutes.

While the rice mixture is warming, whisk together the beaten egg, heavy cream, cinnamon, and nutmeg in a separate bowl until smooth. Set aside.

Once the rice mixture has thickened slightly, stir in the granulated sugar until fully dissolved and incorporated.

With the saucepan still on low heat, slowly pour in the cream and egg mixture while stirring continuously to prevent curdling. Stir until the mixture is well combined and begins to take on a custard-like texture.

Add both types of raisins and continue to stir occasionally as the pudding thickens further, about 5 to 8 minutes. The raisins will plump and soften as they absorb some of the warm liquid.

When the pudding reaches your desired consistency, remove the saucepan from heat. Stir in the butter and vanilla extract until fully melted and fragrant.

Allow the pudding to cool for about 10 minutes, stirring occasionally to prevent a skin from forming on top. Serve warm, or chill for later enjoyment.