• Heat milk, sugar, and cinnamon in a medium saucepan over medium heat. Stir constantly, until the mixture just reaches the point of simmer. Remove from heat.
• In a separate medium bowl, lightly whisk egg yolks. Pour about half of the warm milk into the bowl with the egg yolks, whisking while you do so. Pour the egg/milk mixture back into the saucepan with the rest of the milk. 
• Cook mixture over low heat, stirring constantly, until it thickens enough to coat the back of the spoon.
• Pour the heavy cream into a separate large bowl. Strain the egg/milk mixture into the heavy cream and stir to combine. Stir in the vanilla. Cover with plastic wrap and place in the fridge for at least 4 hours. 
• While ice cream is chilling, make cookie roll dough (it needs to charge for an hour). Right before processing ice cream, make cinnamon swirl mixture. You'll want it to cool, but still be liquid. If it hardens before you're ready to use it in ice cream, heat it in the microwave for a few seconds.
• Once mixture has been sufficiently chilled, process in ice cream maker according to manufacturer’s directions. When the ice cream is almost done hardening, mix in the cinnamon roll cookie dough and cinnamon swirl mixture.
• Scoop ice cream in airtight containers and place in the freezer for another 4+ hours, but ideally overnight.

Cinnamon Roll Cookie Dough

• In the bowl of a stand mixer or a large bowl with a hand mixer, cream butter and brown sugar together until light and fluffy. Mix in vanilla and salt.
• Slowly beat in flour and cinnamon until combined. Stir in milk.
• Refrigerate cookie dough for at least one hour.

Cinnamon Swirl

• In a small bowl, combine melted butter, corn syrup, brown sugar, and cinnamon.