In a small bowl, soak the raisins in the rum for 1 hour.
In a heavy-bottomed medium saucepan, combine the milk, rice, ½ cup (100 g) of the sugar, the salt, and split vanilla bean. Bring to a boil over medium heat, then turn the heat down to medium-low to maintain a simmer. Cover the pan and cook, stirring occasionally, for 30 minutes. Remove the lid and keep cooking and stirring for another 20 minutes, for 50 minutes total, or until the rice absorbs all the liquid. Remove from the heat, scrape the remaining seeds from the vanilla bean into the pudding, and discard the pod. Set the rice aside to cool to room temperature.
Place a rack at the center of the oven with nothing above it and preheat the oven to 375°F (190°C).
Cover the outside of a 9-inch (23 cm) springform pan with one or two layers of aluminum foil (so that water from the water bath you’ll make later will not seep into the pan). Have ready a shallow baking dish into which the pan fits comfortably.
Pour the remaining 1 cup (200 g) sugar into a heavy, dry skillet and shake so the sugar spreads evenly. Place over medium-high heat so the sugar begins to melt without stirring. After about 2 minutes, stir with a wooden spoon until the sugar is dark amber and just beginning to foam, about 3 minutes. Working quickly so the sugar doesn’t harden, remove from the heat and carefully pour the sugar into the prepared springform pan, tipping the pan to coat the bottom and sides as best as possible. Drain the raisins and discard the rum. Stir the egg yolks and raisins into the cooled rice.
Using a stand mixer fitted with a whisk, beat the egg whites on high until foamy, then add the remaining 1 tablespoon sugar and beat until soft peaks form. Fold the fluffy whites into the rice mixture.
Pour the rice mixture into the caramelized sugarcoated springform pan and set the pan in the shallow baking dish. Place the baking dish on the rack in the oven. Pour hot tap water into the baking dish, letting it come about halfway up the sides of the pan. Bake until a knife inserted into the middle comes out clean, about 1 hour and 15 minutes. Remove from the water bath and let cool. Remove the springform ring around the pan, and gently place a serving plate on top of the cake. Invert the cake onto the plate. Let cool to room temperature, then refrigerate for at least 2 hours before serving chilled with soft whipped cream or orange crema inglese, if using.