Preheat the oven to 375F.
Bring the water to a boil in an ovenproof 4-quart saucepan. Stir in the rice and cover. Reduce the heat to low and simmer until the rice is nearly cooked, about 20 minutes.
In a large bowl, whisk together the milk, pumpkin, honey, vanilla, cinnamon, ginger, nutmeg, and salt.
While the rice is still hot, add the pumpkin mixture to the saucepan and stir well to combine. Cover and transfer to the oven. Bake until the liquid has reduced by about a third and the mixture is foamy and bubbling, 45 to 50 minutes. Remove from the oven and stir well to combine all the ingredients. Transfer to a large bowl, then cover and chill in the refrigerator for at least 8 hours or overnight. The pudding will keep for up to 4 days in an airtight container in the refrigerator. Serve with a dollop of whipped cream and a sprinkling of cinnamon.