Step 1In a heavy-bottomed saucepan (preferably ceramic), combine 3 cups of milk with the cinnamon. Bring to a boil over medium heat and cook, adjusting the heat as needed to maintain a simmer, until the milk has reduced to 1 cup and has a slight burnt smell, about 40 minutes. Pour the mixture through a fine-mesh strainer set over a bowl, discard the cinnamon, and set aside until the milk has come to room temperature, 30 to 40 minutes.
Step 2Partially fill a large bowl with ice and water, place a medium bowl in the center of the ice bath and set a fine-mesh strainer across the top.
Step 3Pour the remaining 3 cups milk into the saucepan and bring to a simmer over medium heat.
Step 4Meanwhile, in a small bowl, mix together the sugar and cornstarch. Add this mixture to the cooled burnt milk and stir until the sugar dissolves.
Step 5When the milk in the saucepan reaches a simmer, gradually stir in the burnt-milk mixture, bring to a simmer, stirring constantly, and cook until smooth and slightly thickened, 6 to 8 minutes. Pour the mixture through the strainer into the prepared bowl and stir until cooled. Remove the bowl from the ice bath, cover and refrigerate until cold, at least 4 hours or up to overnight.
Step 6Freeze and churn in an ice cream maker according to the manufacturer’s instructions. For a soft consistency, serve immediately; for a firmer consistency, transfer to a container, cover and freeze 2 to 3 hours until hardened.