Halve the vanilla bean lengthwise and scrape out the seeds; place both the pod and seeds in a medium-sized saucepan.
Add ¼ cup of the sugar, and using your fingers, massage the vanilla into the sugar to help separate the seeds and infuse the sugar.
Add the milk, salt, and cinnamon sticks and bring to a simmer.
Add the rice and cook, stirring often, until almost all the liquid has been absorbed and the rice is very tender, but not mushy, about 40 minutes.
Remove from the heat and discard the cinnamon sticks and vanilla pod.
In a medium-sized bowl, beat the eggs until smooth.
Meanwhile, in a small saucepan, bring the heavy cream and remaining ¼ cup of sugar to a simmer; remove from the heat.
While whisking constantly, add the cream mixture, in a slow and steady stream, to the eggs to temper.
Add the egg mixture to the rice and stir well to combine.
Transfer to a serving bowl, cover with plastic wrap and refrigerate for at least 6 hours, preferably overnight.
Stir before serving and serve with whipped cream and a light sprinkling of cinnamon.
