In a medium saucepan, combine the Arborio rice and 4 cups of milk over medium heat. Stir frequently to prevent sticking.
Once the mixture begins to simmer, reduce the heat to low. Cook for about 20 minutes, stirring occasionally, until the rice is cooked and the mixture is creamy.
Stir in the pumpkin puree, sugar, vanilla extract, cinnamon, nutmeg, and salt. Mix well to combine.
Continue to cook on low for an additional 5-10 minutes, while stirring frequently, until the pudding reaches a desired consistency.
Remove the saucepan from heat and stir in the butter until melted and well incorporated.
Allow the pudding to cool slightly before serving. You can serve it warm or chilled, topped with chopped nuts or whipped cream if desired.
For added flavor, you can include a pinch of ginger or cloves.
Store any leftover rice pudding in the refrigerator for up to 3 days. Reheat gently on the stove or in the microwave, adding a splash of milk if necessary to restore creaminess.