In a medium saucepan, combine the milk, heavy cream, vanilla extract, and cinnamon. Heat over medium heat until the mixture begins to steam, but do not boil.
In a separate bowl, whisk together the sugar and egg yolks until the mixture is pale and creamy.
Slowly pour one ladleful of the warm milk mixture into the egg yolk mixture, whisking constantly to temper the eggs.
Pour the tempered egg mixture back into the saucepan with the remaining milk. Cook over low heat, stirring constantly, until the custard thickens slightly (about 5-7 minutes). Do not let it boil!
Remove from heat and stir in the cream liqueur. Let cool completely at room temperature, then refrigerate for at least 4 hours to chill thoroughly.
If using an ice cream maker, pour the chilled mixture into the machine and churn according to the manufacturer's instructions. If not, pour the mixture into a freezer-safe container and freeze, stirring with a fork every 30 minutes to break up ice crystals.
Before serving, let the ice cream soften at room temperature for a few minutes to make it easier to scoop. Garnish with a sprinkle of cinnamon and chocolate shavings, if desired.
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