Warm the milk, sugar, 1 cup of the cream, and the salt in a medium saucepan. Scrape the seeds from the vanilla bean into the warm milk and add the bean as well. (If using vanilla bean paste, add the paste at this point.) Heat over medium-high, stirring occasionally, until the mixture is warmed through. Cover, remove from the heat, and let steep at room temperature for 30 minutes.

Pour the remaining 1 cup cream into a large bowl and set a mesh strainer on top. In a separate medium bowl, whisk together the egg yolks. Slowly pour the warm mixture into the egg yolks, whisking constantly, then scrape the mixture back into the saucepan.

Stir the mixture constantly over medium heat with a heatproof spatula, scraping the bottom as you stir, until the mixture thickens slightly and coats the spatula (about 170 ˚ -175 ˚ F). (This takes about 10 minutes.) Pour the custard through the strainer and stir it into the cream. Put the vanilla bean into the custard, add the vanilla extract and cinnamon, and stir until cool over an ice bath.

Chill the mixture thoroughly in the refrigerator. When ready to churn, remove the vanilla bean and then freeze the mixture in your ice cream maker according to the manufacturer’s instructions. When the ice cream is almost done churning, add the chopped shortbread cookies. Remove from ice cream maker and store in an air tight container in the freezer. Freeze a few hours to firm up before serving.