How to Make It
Add the milk to a medium bowl. In another medium bowl, whisk together the yolks, ½ cup of the sugar, and salt. Combine the cream and the cinnamon in a medium saucepan and bring to a simmer over medium-high heat.
Whisking continuously, add the hot cream mixture to the yolk mixture a little at a time. Continue whisking until well-combined. Return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until it is just thick enough to coat the back of a wooden spoon, 3 to 4 minutes. (If you can draw a line through the custard on the back of the spoon and it holds its shape, then the mixture is ready.)
Pour the custard mixture through a fine mesh sieve into the bowl of milk. Cover with plastic wrap and set in the refrigerator to chill until very cold, at least 12 hours. Place an empty metal loaf pan in the freezer to chill.
In a large skillet, melt the butter over medium heat. Add the remaining ¼ cup sugar and cook, stirring occasionally, until the sugar turns a deep golden brown, 2 to 3 minutes. Add the apples and cook until the apples are tender and the liquid is smooth, 2 to 3 minutes. Transfer the mixture to a plate and cool completely.
Pour the chilled custard into an ice cream maker and process according to the manufacturer’s instructions. When frozen, scoop ⅓ of the churned ice cream into the prepared loaf pan. Top with ⅓ of the cooled apple mixture. Repeat this process two more times, then use a butter knife to swirl the apple mixture throughout the ice cream. Wrap the loaf pan with plastic wrap and freeze until firm, at least 6 hours.