In a heavy saucepan, combine the whole milk and sugar, heating the mixture until bubbles form around the edges. Gradually whisk a small portion of this hot mixture into the beaten eggs, then return everything to the pan. Continuously stir over low heat until the mixture reaches a temperature of at least 160°F and adequately coats the back of a spoon.

Once the desired temperature is achieved, remove the saucepan from the heat. Transfer the custard to a bowl and place it in an ice water bath, stirring for approximately two minutes. After cooling, incorporate the heavy cream, ground cinnamon, and vanilla extract. Cover the surface of the custard with waxed paper to prevent a skin from forming, then refrigerate for several hours or overnight.

When ready to churn, fill the ice cream maker's cylinder two-thirds full with the prepared custard, following the manufacturer’s instructions for freezing. Keep any remaining mixture refrigerated until you are prepared to churn it. After churning, transfer the ice cream to freezer-safe containers, ensuring to leave space for expansion. Freeze until firm, which may take 2 to 4 hours.