Stir sugar and half-and-half together in a saucepan on medium-low heat, then remove when the mixture starts to simmer.
Add the cream mixture to the eggs and whisk quickly so you don’t scramble the eggs; then, pour your egg mixture into the saucepan and stir in the heavy cream.
Cut the vanilla bean in half along its length, scrape the seeds out, and add the roots and the bean to the cream mixture.
Set the mixture back on medium-low heat and stir until you get a consistency that can cover the back of a metal spoon completely.
Take the mixture off the heat and strain with a mesh sieve into a bowl, whisk in the cinnamon, and set aside to cool. After the mixture has cooled, cover and let refrigerate overnight or for several hours until properly chilled. (You can place plastic wrap over the surface so that skin doesn’t form).
Pour the cold mixture into your ice cream maker and refrigerate according to the manufacturer’s instructions.