Make the Ice Cream Base In a saucepan, heat the milk, cream, sugar, salt, and cinnamon stick over medium heat until steaming, but not boiling. Keep it simmering on low for 30 min.
In a separate bowl, whisk the egg yolks and sugar until pale and fluffy.
Slowly pour some of the warm milk mixture into the yolks while whisking (to temper them), then pour the yolk mixture back into the saucepan.
Cook on low heat, stirring constantly with a rubber spatula, until the mixture thickens slightly.
Remove from heat. Stir in the vanilla extract and remove the cinnamon stick.
Let the custard cool a bit, then refrigerate for at least 1 hour or up to overnight, until fully chilled.
Make the Blueberry Swirl
In a small saucepan, combine blueberries, sugar, water, cornstarch, and lemon juice.
Bring to a simmer and cook for about 5–7 minutes, stirring occasionally, until thickened and jammy. Let cool completely, then refrigerate.
Make the Cinnamon Roll Cookie Dough
In a bowl, mix the butter and brown sugar until smooth.
Add in vanilla, cream, salt, and cinnamon.
Stir in the flour until a dough forms.
Roll small balls of dough (like mini cinnamon roll bites) and then roll them in pearl sugar, then place them on a tray. Freeze until firm.
Assemble the Ice Cream
Pour the chilled custard base in an ice cream maker while it’s spinning.
When it’s almost done churning, fold in the frozen cinnamon roll dough bites.
Transfer half of the ice cream into a container. Spoon some blueberry swirl on top and gently swirl with a spoon. Add a couple cinnamon bites between the layers.
