In a small bowl, combine sugar and scraped vanilla seeds (reserve remaining vanilla pods for another use), and rub sugar between fingertips to disperse vanilla seeds. Sift mixture into 3-quart saucepan to remove any fibrous remnants from the scraped vanilla pod. Add milk and whisk until sugar is dissolved. Stir in rice and salt.
Bring mixture to a boil over medium-high heat, then immediately lower heat to simmer. Cook, stirring and scraping bottom and sides of pot every few minutes with a rubber spatula to prevent sticking and scorching, adjusting heat as needed to maintain gentle bubbling, until mixture begins to thicken, about 45 minutes. Continue cooking, stirring every minute, until rice pudding thickens to the consistency of yogurt and coats the back of a wooden spoon, about 10 minutes longer. Remove from heat.
If serving warm: Divide rice pudding between individual serving bowls, and serve. If serving cold: In a large bowl, set up an ice bath by partially filling it with a combination of cold water and ice. Transfer rice pudding to a medium bowl, and set bowl inside prepared ice bath. Allow to cool to room temperature, stirring occasionally with a rubber spatula, about 30 minutes, then refrigerate pudding until completely chilled, about 2 hours (discard ice bath). When ready to serve, whisk or stir pudding until smooth, adjusting consistency as needed with up to ¼ cup (60ml) extra milk. Serve.