In a medium saucepan, combine the heavy cream, 1/4 cup of the sugar, the vanilla extract, salt and cinnamon sticks. Bring to a boil, turn off the heat and let sit.
In a small bowl, combine the egg yolks and the remaining 1/4 cup sugar and beat to a homogeneous consistency.
Bring the heavy cream-cinnamon mixture back to a boil and turn the heat off. Whisk a third of the heavy cream mixture into the egg-sugar mixture, and then immediately whisk the egg mixture back into the remaining heavy cream mixture. Bring the mixture back up over medium heat, stirring constantly, until thickened and coats the back of a spoon, about 10 minutes. Strain the mixture and chill over an ice water bath.
Churn the chilled mixture in an ice cream/gelato machine according to the manufacturer's directions.