For ice cream base: Bring milk just barely to a boil in a medium saucepan. Add vanilla beans (sliced lengthwise and seeds scraped), cinnamon chips, and sugar. Stir until sugar is dissolved. Stir in cream and half and half. Remove from heat and let steep for 20 min. then strain into a clean bowl. Cover and refrigerate until well chilled.
For vanilla crunch: Preheat oven to 350 degrees. Mix vanilla sugar with butter until well combined. Spread sugar mixture evenly on a parchment- or silicone-lined baking sheet. Bake until just crisp, about 15 min.; let cool completely, it will crisp up more as it cools. Break into small pieces and set aside.
To make ice cream: Pour chilled cream mixture into an ice cream maker and process according to manufacturer's instructions until churned and thick. Transfer ice cream to a bowl and fold in cinnamon crunch mixture. Transfer to an airtight storage container and freeze until set, at least 4 hours.